If the tire is a true 35 inches, likely 34.8, I'm afraid that it will be too tight. There just isn't enough room between the last two cross members for a tire larger than 34.25 inches.
Before building these kits, I just wanted a spare that tucked up and out of the way which is why I went with a narrow Swamper on a 6 inch wide trailer wheel.
Other advantages include:
A. Getting to the spare is a pain so I don't worry about putting it in the rotation.
B. It's 3 inches narrower than my 315's which gives me that much more clearance.
C. It tucks up completely so you can't see it, so nobody knows that it is a different style than the 4 on the ground.
D. Most importantly, I usually get tired of the tires before they wear out and a fifth tire in the rotation makes them last 20% longer.
E. The Swamper is very close in size to my 315's so in the event I need it, it won't cause any damage to the drive train.
If you use a worn 315, say with half tread, and your receiver doesn't encroach on this space too much, then yes it will work, but again I wouldn't put a half worn tire into the rotation.
Another option I just thought of is to deflate the tire before winching it up. It would probably be small enough to fit, but this would require a way of filling it up when you need it.
With another inch of clearance, fitting a 315 wouldn't be an issue.
Let me know if I can help.
Adam