Of course they do just like any other animal. They just have to deal with it differently then domesticated animals do, because they don't have someone to apply Frontline, Atvantage, or any other kind of flea and tick remedy. Squirrels, bats, birds, possum, etc. etc. all have flea and tick problems, either they survive them or they succumb to them, which ever the case may be.
In a very young animal it can cause severe anemia, in an older animal it is just plain miserable, but once the first frost comes and the fleas and ticks die off, they get the relief they have long awaited.