No, a gimbal tripod head WILL NOT WORK with your camera and usually isn't a good choice for birds in flight, in particular.

Gimbals are designed for use with lenses that have tripod collars. Those are typically only found on interchangeable telephoto lenses (for DSLRs and mirrorless). I'm not aware of any "bridge camera" like yours that has a tripod mount collar on the lens.

In fact, it would be impossible to mount your camera to most gimbal heads.

Gimbal heads also are generally best used with very large and heavy lenses. They work well with 300mm f/2.8 and larger. I regularly use with a 100-400mm too, though it's doesn't "balance" quite as well on the gimbal, as do heavier and longer lenses. I do not use my gimbal heads with 70-200mm f/2.8 and 300mm f/4 lenses that are around 3 lb. or less. They balance very poorly on a gimbal.

For birds in flight, I find hand holding best. There are exceptions, of course, but most bird flight is too erratic to follow well with a lens on a tripod, regardless the type of head being used. MAYBE a monopod... I use one sometimes for sports such as auto racing, equestrian events... But those subjects are also moving along predictable paths, unlike most birds.

Several responses above praise various gimbals or their use in general... and they aren't wrong. Gimbal heads can be very useful with the right cameras and lenses. However those earlier responses didn't consider the camera you're using. They simply aren't made for use with non-interchangeable lens "bridge" cameras like your RX10.

EDIT: In a followup you mention that your camera is light weight. Many people actually find that "lighter" often doesn't translate into "steadier" shots. In fact, I add battery grips to my DLSRs in part to increase their weight and mass, for steadier shots. (This also helps the camera balance better when fitted with a large lens on a gimbal head. Of course, the grip also doubles battery capacity, provides a comfortable means of holding the camera in vertical orientation and provides a secondary set of controls.) I currently use five "full size" DSLRs for work, each of which weigh around 2 lb. for the camera and grip alone... plus the weight of any lens (some of the largest of which weigh 8 lb.) I also have a small mirrorless "travel, hiking, street photography" kit... a body with four compact lenses and a few accessories... that entire kit weighs less than even one of the DSLRs with one of the more moderate size lenses. Frankly, I find it a lot more difficult to get a steady shot hand holding that little mirrorless camera, versus hand holding one of the DSLRs.

So, @SuperflyTNT’s message didn’t resonate with you? Did you not also read @Amfoto1’s reply? what @MDI Mainer proposed is utterly ridiculous for the camera the OP states he has.

In fact, in your retort above you state "Well I don't think most super zooms on the market today are IF” and go on to surmise that because a big piece of glass like the Tamron (or indeed, the Fuji 100-400 I use on a gimbal head) changes the center of gravity so why not a bridge camera, whose lens alters the center of gravity an order of magnitude or more than the mentioned lenses? That is, it is significantly different than the Sigma or Tamron are.

Have you actually used any of this gear, or are you only trying to make us think you are smart?

What we have here is a classic case of the perfect being the enemy of the good (and possibly a tinge of gear snobbery as well).

Yes the camera and lens are supposed to be perfectly balanced on the gimbal, and yes this can best be achieved with an internal zoom lens attached by a lens collar and foot. But the gimbal function can still be useful (and better than any alternative) where the balance point shifts as the lens barrel length changes, or there is no lens foot and an alternative to using the camera body's tripod mount must be improvised.

After all, if we're strong enough to hold a camera we're strong enough to overcome the force of gravity on a out-of-balance gimbal rig!

So as far as I'm concerned simply saying that it can't be done or won't work just evinces a lack creativity and ingenuity. And yes I've successfully used a similar rig on a Sony A6000 and 18-200mm lens, jacked to 400mm using CIS, so a 600mm FF equivalent.