The rims are probably ok- i mount 1.95" MTB tires on 19mm rims.
The bigger question is clearance for the tires- they're a bit bigger than most 35's, and may have clearance problems, especially with the front brake (which you need, fixed gear or not). Rubbing carbide studs is not what you want.
If the bike was built for 27" tires, then you're probably set to go.
fatbat.