We have two cats that were also our "babies" before we brought our daughter home. One we classify as a scardy cat and the other "rules the roost" so to speak. We've had no problems with either one, except that they tend to go into hiding more now.
Our scardy cat is actually the one that's gone around the baby and that's only if we're holding her. It's taken the other cat about 4 months to even go in the baby's room (again, only when we're in there because she totally runs at the first sound our daughter makes whether it be a sneeze or a yowl
). We never had any problems with either claiming territory, but then they never showed any inclination before, either (except around the food dishes, and that just consisted of "scratching" the floor and pushing each other away). We did have both cats fixed when they were old enough, so again, we never had problems with spraying or such. At night we do put a baby gate up infront of the baby's door so the cats don't go in there at night (they were taught from the time they were brought home that they're not to jump the gate). Yes, they could jump the gate (and have into our room, but usually only when they're scared - they like to hide under our bed, always have). LOL! Our cats learned from the first night that babies are noisy, and they never have cared for loud noises.
Naturally, you'd want to watch your cat around the baby, but I think chances are good that you're cat will just give the baby a wide berth if anything, especially if s/he's never shown any aggression towards others.