The triggers usually require some filing before they'll drop in. Hammers generally will go in the gun without having to fit them, but it could throw other things out of whack like your thumb safety.
That doesn't mean you will have a functional or safe firearm afterwards, however. If something is out of spec, you can have hammer follow or a complete full-auto experience.
Before live fire, I suggest checking for hammer follow by dropping the slide on an empty chamber a few times. At the range, load one or two rounds at most into the mag, for the first 4 or 5 mags.
While many owners get lucky and never have problems, there are a lot of caveats and subtleties that can bite you if you don't know what you're looking for. The trigger bow can be too long, which can cause trigger bounce, which can cause hammer follow. The overtravel adjustment must be properly set or the trigger can go back too far and lift the sear spring off the hammer leg, leading to hammer follow or full auto. The hammer may not form a safe engagement angle with the sear, which may need to be altered in order to be back in spec.
I strongly recommend doing a lot of reading and research before changing anything. Even better, get an experienced 1911 smith to at least check the gun afterward, if not perform the work.