BebuLamar

The condition that you describe I would estimate is of the light level of EV 5 to 6 @ ISO 100. If you are able to expose with flash at several stops more than the color balance of the ambient light won't be an issue. But your distance seems to be quite far. I would do test shot in advance.

anotherview Loc: California

You describe a mixed lighting environment. You might try the auto white balance setting. Later, in Photoshop, adjust the WB to eye. Apply this adjustment to all your photographs.

I sense that the flash lighting will function as fill lighting, to avoid the racoon-eyes effect from overhead lighting indoors.

ABJanes Loc: Jersey Boy now Virginia

Well Done! The OP could visit with a friend before the event taking simulated test shots.......tables, groups, headshots. Keep settings on an index card & distances. The best part of balancing the ambient and slightly underexposing is the flash is a softer touch of light, which helps for more natural fleshtones. Adjust as needed with FEC on flash head after enlarged chimping also viewing the histogram & blinkies as well.

Architect1776 Loc: In my mind

As Notorious stated, use settings that negate the ambient light.
The SB 800 is an excellent and pretty powerful flash that should have no problem with most shots.
This being said go back to the venue and try shooting with it at low ISO and smaller apertures and see what happens.

lamiaceae Loc: San Luis Obispo County, CA

If you have trouble with the WB with the mixed Fl & flash colors be sure you shoot RAW. Yes, see if you can overpower the Fls with your strobe. Use highest syn speed available on your camera.

larryepage Loc: North Texas area

Actually, because the fluorescent lights are plasma lights, a shutter speed of 1/60 or slower is necessary to avoid flicker effects...

And...we haven't mentioned...the SB800 will zoom to your lens focal length, up to about 100mm or so, if you are using a compatible lens.

aphelps Loc: Central Ohio

If your exposure requires the flourescent lights to be on, you might experiment with custom white balance settings to offset the color shift in the mix of ambient and flash lights. If your camera has an instant custom white balance feature try that as well.

ABJanes Loc: Jersey Boy now Virginia

Here's another approach.......https://neilvn.com/tangents/fluorescent-lighting/

Bubbee Loc: Aventura, Florida

Try a high (up to 4000) iso with your flash (fill) turned sideways or backwards. FYI your SB 800 TTL won't sync with iso over 1000 so use M. I have the D7100 and SB800 and it works for me, and I learned this from local pro's. Try it yourself beforehand, please!

Morning Star Loc: West coast, North of the 49th N.

You still have a week or so before Valentine's. Why not go to the church, ask the custodian to turn on the lights as they will be for the banquet, then take a number of test shots at different settings.
The beauty of digital is that you don't even have to take notes, all the info you need will be in the exif info.

gvarner Loc: Central Oregon Coast

With flash, there are two sources of light, the flash and ambient. Proper settings can kill the effect of ambient light. More on this later. Then there is distance. Your SB 800 has good reach and proper settings can help with this. And for settings, I would use flash in TTL mode, camera in Manual, ISO at 400, shutter at 1/200, aperture at F4.5. The TTL feature of the flash will give proper exposure on the subject as the ISO or Aperture are changed. The high shutter speed will kill the effect of the fluorescent lights. The ISO can be increased to gain some reach for the flash. The Aperture can be stopped down to increase DOF.

For distant shots, you may want to put your flash on a tripod and use a radio trigger to get your light closer to the subject. The TTL flash will still give proper exposure on the subject. I haven’t tried this setup but I don’t see why it wouldn’t work since the flash itself is controlling the exposure.

GoofyNewfie Loc: Kansas City

The pop-up flash on the OP’s Nikon D7200 can trigger and control the SB 800 remotely.
Probably no need for a radio trigger in this situation so long as the receiver on the flash is pointed toward the camera.

http://darrellyoung.blogspot.com/2011/10/understanding-flash-commander-mode.html?m=1

JayRay Loc: Missouri

Other than getting your exposure correct, your big issue will be white balance. Get there early to set all of this up and test it. There are three ways you can do this (with #1 being easiest):
1. Shoot in Raw so that your white balance can be better tweaked in post production and set camera on Auto white balance. Shoot with flash in TTL mode and with center weighted metering on your camera and dial down flash 1/3 to 1/2 stop. On the first shot at each significantly different distance, do a quick test shot by having someone hold a gray card or white card near the center of the shot (only for the throw away test/reference shot) that you can reference during post production to set your white balance.
2. OR: Shoot with flash in TTL mode and with center weighted metering on your camera and with a white (or gray) card, do an in camera custom white balance for each significantly distance that you are shooting with the ambient fluorescent lighting on and supplemental light from your flash dialed down 1/3 to 1/2 stop. I would organize your shoot such that you minimize the number of times that you have to significantly change your shooting distance. Each time your distance changes significantly you must redo your custom white balance.
3. OR: If you can wirelessly trigger your flash: set your camera on manual mode and your flash in manual mode (not TTL mode), set your flash on a stand or tripod (do not move the flash during the shoot), figure out your exposure, do only one custom white balance and then only change your shooting distance to your subjects (keeping your subjects at the same location, do not move your flash during the shoot, but only move your camera location).

gvarner Loc: Central Oregon Coast

True. I was thinking of the radio trigger being more versatile, long distance, doesn’t require line of sight. With my D7000 and SB600, the sensor on the flash has to be towards the camera.

GoofyNewfie Loc: Kansas City

Yes, I use radio too but the OP already has the capability built in to his system. Without seeing the room, it’s hard to say, but the IR signal is pretty sensitive.