First of all, crop factor isn't magnification- that's an important point.
Secondly 300mm is ok if you want to shoot seagulls or tame birds, it's not enough for serious bird photography. If you look at my Fine Art Nature galleries, you'll see mostly large birds or small birds in close-approach settings (and I have boatloads of bird pictures that aren't in that gallery.) All of them were taken with lenses that went to at least 400mm, often 500mm on a 1.5x crop-factor body (Fuji S2Pro or Nikon D2x.) That's an effective angle of view starting at 600mm and ending up at 750mm.
Thirdly, even with relatively large birds like Bald Eagles, many of my images are further crops. Even with the 1.4x TC on a 400mm lens (560/4) some are crops. The 1.7x TC's degradation doesn't hold up as well, or I'd probably shoot with it more than 30% of the time (680/5.6) despite the light it needs (I use it less than .1% of the time now.)
At Conowingo Dam in Maryland you could actually get usable Bald Eagle shots, as well as at Homer, Alaska and perhaps a lock in Iowa. Outside of that, I've been close enough to a Red Shouldered Hawk twice where a 200mm could get a fairly good in-situ photograph. If you can find a regularly peopled place with a juvenile Great Blue Heron, 200mm would be close enough (Great Falls, Maryland, Huntley Meadows, Virginia are the two places I've been where that would work,) but an adult wouldn't let you get anywhere near close enough. At Cape May, New Jersey you could get shots of Mute Swans with a 200mm lens, though they'd be small in the frame (environmental portraits if you will.) At Skyline Drive in Virginia you could get plenty of deer pictures if you're patient and position yourself well so the deer drift towards you as they graze in the morning, and you can pretty much get any deer picture you want from out a car window as they expect to be fed. That's really the class of things you can expect in the US. If your stated purpose is wildlife, you need to be twice as close with a 200mm lens as with a 400mm lens, crop factor or not.
I'm not saying that you couldn't use blinds, or you couldn't build fantastic stalking skills- but you'd miss more shots than you'd get at 200mm.
The Canon 70-200 f/4 is a fantastic lens for its price, but it's not a good wildlife lens. I'd encourage you to rent one for a week and try to shoot some birds, especially now during winter when they'll actually come up to food and see how it goes- then rent a 100-400 and let me know what you think of the difference between the two, as well as how many shots you get where the birds stick around vs. fly away. Alternately, rent the 100-400, shoot at 200 for two days and 400 for three days and compare the results, even in the back yard with seed on the ground. Make sure you try to get a few dozen flight "action" shots too. Finally, spend a day chasing something in your local "Rare Bird Alert" report- granted a lot of that sort of thing will be easier in the spring and summer, but doing it in the winter will let you know how challenging it can be. At the end of a week, you should have a lot more valuable advice to give a potential bird shooter.
Please note, I'm not being sarcastic, I'm actually encouraging you to try it- you may end up with a new shooting hobby, but you'll definitely learn a thing or two and I promise it'll be valuable experience.