With our first son, we started signing haphazardly around 8 months, and he picked up a few within a couple weeks (milk, mommy, bed). He was an early talker, so he never really used the signs much, but we used them a lot (at a noise play place, for example) By about 18 months the signs were completely gone because his verbal vocabulary was so huge.
Our second son has hearing loss and several birth defects that cause him to be essentially non-verbal. We didn't start signing until 11 months (only because we were so focussed on his other health needs, communication was low on our priority list frankly). He picked them up slowly at first, by 18 months he had maybe 10-15, but by age 2 he had over 100, and now at almost 3 he has close to 200 signs!! He is fully age-appropriate with his communication (if you counted his signs as verbal words, his vocabulary is age appropriate, he strings them together to form multi-word sentences, he even "hand babbles" where he makes up a sign if he doesn't know the correct sign)
Since we sign with our middle son, our older son has started signing again (and has just as big a sign vocabulary as his brother) and our baby is being exposed to sign. At 4 months old he's not doing any on his own yet of course, but I wouldn't be surprised if he starts doing them between 6-9 months just because he has so much exposure.