All the 150-600mm lenses have variable f/5-f/6.3 maximum apertures.
Adding a 1.4X teleconverter to a lens "loses" one stop of light. So any of the 150-600mm with 1.4X would become "210-840mm f/7.1-f/9" lenses.
Most DSLRs cannot autofocus any less than f/5.6 aperture. (Note: the f/6.3 of these lenses "pretends" to be f/5.6, to fool the camera into focusing.)
I believer you use a Canon T3i, which is "f/5.6 limited".
A few Canon, especially newer models, are "f/8 capable". Those include all the 1D-series. More recently the 5DIII and now 5DIV are able to AF f/8 lens/TC combos. The 7D Mark II was the first of the APS-C Canon to be able to do so, too. Now all the cameras using the 45-point AF system introduced in the 80D can, too... that includes the T7i, 77D, 6D Mark II and 90D. All the current full frame Canon are f/8 capable, too.
Bultaco wrote:
The 150/600 G2 on a D500 with the TC1.4 will af at f8 with good lighting.
And, yes, some Nikon are "f/8 capable" too.
But your T3i isn't.
HOWEVER, even a DSLR with f/8 capability won't help when the lens' max aperture drops below that.... as will be the case at the longer focal lengths of the 150-600mm lenses, which are what you'd be using. After all, you're not adding a 1.4X to make 150 into 210mm... you're adding it to make 600mm into 840mm!
AND, in most cases f/8 capabilities are limited to one or just a few AF points. For example, in the 7D Mark II it's the center point only (out of the camera's 65 points). On 80D/77D/T7i/90D/6DII it can be up to 27 points, depending upon the specific lens/TC combo (it's 27 points only with the 100-400 Mark II and 1.4X III, as far as I know).
The Sigma 150-600mm "Sport" drops to f/6.3 around 320mm. The Sigma 150-600mm "Contemporary" stops down to f/6.3 around 380mm. And the Tamron 150-600 "G2" steps down to f/6.3 around 420mm.
With a 1.4X attached, any of those lenses would be less than the f/5.6 your T3i needs at all focal lengths. With f/8-capable cameras, AF should work up to that point, at least.
I really don't know if the lens will also "fool an f/8-capable camera" into trying to autofocus at f/9.... or how good the AF would be, for that matter. It's very likely to struggle and hunt, in all but the best lighting conditions.
There are reasons people spend $10,000 on 600mm f/4 and 800mm f/5.6 lenses!
BTW, the EOS R and RP mirrorless cameras are said to be "f/11 capable". They are able to focus in much lower lighting conditions, so are also able to AF more extreme lens/TC combos.
BUT...
None of the above talks about image quality, which is likely to drop off dramatically with zooms like the 150-600s if they are combined with a teleconverter. Very generally speaking, IQ tends to drop around 5 to 10% with a 1.4X and roughly 10 to 20% with a 2X. It's usually best to combine a teleconverter with a lens that's exceptionally good to start with... such as a prime (instead of a zoom). There are a few exceptions. The Canon 300mm f/4L IS USM works very well with either Canon 1.4X II or III. There's only minor loss of IQ. The EF 100-400mm L IS USM "II" also works extremely well with either of those 1.4X teleconverters... there's almost no change in IQ at all. The Canon 70-200mm f/2.8 II or III also work well with either of those 1.4X and even very well with the Canon 2X III. But none of these really get you the "reach" you appear to be seeking.
There are myriad possible combinations of teleconverters with telephoto zooms and primes. There's "compatibility", meaning the teleconverter will fit and theoretically the combo will be able to autofocus, albeit slower and more inclined to hunt.... And there's real world "usability", where image quality is acceptable, too. Unless you can find someone using the specific lens and specific teleconverter combo you're considering, it's difficult to predict what will work well together to produce images you're happy with... and what won't.
Frankly, although I certainly haven't tried them I'd hesitate to recommend any of the 150-600s with teleconverters, even if you had a camera capable of autofocusing the combo. I just think the combination is likely to disappoint when it comes to IQ. But, who knows. Maybe the results would be better than expected or would be acceptable to you, even if they aren't to me.
However, you're already using an APS-C camera, which itself acts a bit like a "free 1.6X" teleconverter. Putting a 150-600mm on that T3i - without any TC - is much like using a "240-960mm" lens on a full frame camera. AND, that's without any of the light lost to an actual teleconverter. I.e., it's with no change to the lens' effective max aperture. That "240-960mm" will still be f/5-6.3 and able to AF on your camera.
What I'd recommend...
Get closer to your subjects! Or get them to come closer to you (with food attractants, calls or decoys). Nearly "1000mm" effective focal length is a real handful to work with. You will need a tripod for steady shots and just because your arms will get tired shooting for anything more than a few minutes. I'd recommend a quality tripod with a gimbal, which are designed specifically for large lenses. You will be shooting more distant subjects through more atmosphere, which can really mess with image quality too... and you can't do anything about it.
I use Canon 1.4X II and 2X II teleconverters with some lenses.
I use the 1.4X on 135mm f/2, 300mm f/4, 100-400mm II, 300mm f/2.8 and 500mm f/4.
I use the 2X on 300mm f/2.8 and 500mm f/4 (the latter combo is f/8, so can only AF on select cameras listed above).
I've experimented with both TCs on various older 70-200s and won't use them together... but I don't have the latest III version TCs or the 70-200/2.8 II or III lens. Those are said to work better in combination.