You getting your film processed before I do Hersh, now there's a laugh unless you drive back into Kalamazoo, wait on it to get done and then drive back to Indiana using your get outa speeding tickets badge faster than I can cover the 7 miles from Kal Color to home... Up to the challenge???
Jen, I'd buy the fastest lens you can afford - primes work better with teleconverters than a faster zoom - and you should use a teleconverter specifically intended for/matched to the lens in question. What I posted was shot with a Nikkor 300 mm f/4 AF-S lens coupled to one of my F5's via a Nikkor TC-14E AF-S teleconverter, which gave me an effective focal length of 420 mm and a max apeature of f/5.6. The TC-14E and TC-20E AF-S teleconverters that I have DO NOT work on non AF-S lenses, so be careful that you don't get into a lens/teleconverter incompatability issue with whatever you buy. Pushing Provia 100F slide film 1 stop to iso 200 I was still shooting between 1/640th and 1/800th sec most of the time with aperatures in the range of f/6.3 - 7.1. Yes, that would be fast enough having a 400 mm f/5.6 lens to directly answer your question. One alternative might be Tamron's 200-400 mm f/5.6 zoom, It's a constant aperature f/5.6 lens across the entire focal range. Prices aren't too stiff, ~$450-500, the lens is decently sharp and it's a push-pull zoom with a good lens hood. I have one although I don't use it all that much any more. It is convenient when you're out in a gale and can't change lenses because of blowing sand but need a different focal length. I have gotten some very good stuff with this lens in the past. It also couples nicely to Tamron's autofocus 1.4X and 2X teleconverters if that's an issue. You can stack those to get you out to 1140 mm if you need something really long although the max aperature is something like f/16