The answer is: perhaps, but not as much as you'd think. Full frame lenses are at their best in full frame cameras. While they can be used for crop sensor cameras too, they are not optimized for this use. So, the benefit may be there but it's not 2.56 times more pixels.
Let's take a look at the lens on DxOmark.
DxOmark for 100-400L IS USM lens gives these perceptual megapixels (P-Mpix) counts:
- 760D: 7 P-Mpix (24 Mpix sensor)
- 5DIII: 13 P-Mpix (22 Mpix sensor)
- 5DIV: 14 P-Mpix (30 Mpix sensor)
Considering the smaller sensor size of 760D, one needs to do a 1.6x crop (in length units), or 2.56x crop (in areal units) on the
full frame 5D figures to obtain the same area. Thus, the equivalent figures for 5DIII and 5DIV are 5.1 P-Mpix and 5.5 P-Mpix. Normalizing for sensor megapixel count (24 Mpix is 75% of 22 Mpix + 25% of 30 Mpix), we get 5.2 P-Mpix on full frame with a 24 Mpix sensor.
So, yes, a crop sensor camera has some advantage here but not as much as you'd
expect. 7 P-Mpix / 5.2 P-Mpix = 1.35 (approximately), so instead of getting 2.56 times more perceptual pixels, you get only 1.35 times more perceptual pixels.
Furthermore, a practical detail: when trying to photograph flying birds, it's hard to get the bird to the viewfinder with a 250mm lens on a crop sensor camera because of the long focal length. A 400mm focal length would be even more insane, making it hard to aim the camera. So, a full frame camera would probably be a better choice to use with this lens, when photographing flying birds: aiming the camera is somewhat easier, and the final photo can be cropped at a minor cost in perceptual pixel count.
However, when taking photos of the moon, a tripod can be used. With a 250mm lens on a crop sensor camera, one can clearly see the rotation of the Earth, but this is mainly a minor annoyance rather than a major problem when taking multiple photos of the moon. A 400mm lens on a crop sensor camera would not be a problem in this case, and the 1.35 times more perceptual pixels would create a slightly sharper image.
If the full frame camera is a mirrorless one (such as EOS RP), there's always the option of using a teleconverter. Autofocus doesn't work with DSLR + teleconverter unless the aperture number is at most 5.6 (there may be some exception cameras to this rule allowing f/8 autofocus), but on a mirrorless camera, f/11 should work with autofocus.
Moreover, one more thing to consider: the 100-400L lens, like most lenses, is sharpest in the center of the picture. I didn't take this into account when calculating the 1.35 times benefit. It may be the case the 1.35 times benefit diminishes to equality when cropping at the center of the frame, which is the sharpest location.
An interesting observation: the cheap 55-250mm has on the 760D 8 P-Mpix, but the focal length does not go up to 400mm.