I've had six full ms requests and they breakdown like this (from best to worst)
1. ten days
2. thirty eight days
3. One hundred and two days.
4. One Hundred and eighteen days
5. Two hundred and seventy three days and still counting...
Numbers one to four all said it could take up to three months to get back to me, so it wasn't my intention to contact then until the three months were up.
6. Didn't hear for over five months, sent a very polite email asking, and was told the intern looking at it had left, had passed it upwards, but it was overlooked. Then waited another three months, another polite request, and they said no about three weeks later. (I am number six is all on my old computer, the dates pretty approximate, but the magic three months was in there.)
Whatever they say on the website, go by. If they say in their request it will take three months, then believe it. I wouldn't enquire after three months and a day, I'd (as you can see above) leave it a bit longer, and then be very polite and say you hate to be seen to hassle, but have they had a chance to read it? As brief as possible I think, though wait for others to add their advice.
ps: saw your post. I did continue to edit and rewrite certain scenes while I waited, because it was improving it... Made me feel silly thinking 'damn, they'll think I submitted before it was ready' but I even had feedback from an agent that this was acceptable, as long as I wasn't changing the story too much.