We had our third son in August and it was fine - great in fact!
He was born 2.5 weeks before the start of term. DS1 was starting year one and DS2 was still at home with me (only 3 - so slow to walk to school/get out of the house etc). Plus, in DS3's third week DH started working away from home again one night a week.
It has been fine. You'll be amazed at how little sleep you can survive on when you have to, and how quickly you can get out of the house when you have a deadline. With DS2 it used to take me ages to get out of the house (if I didn't have a deadline) - now we are out by 8.30 (ish).
Tips: Try to get your DH/DP to stock up on some holiday so that every 2 or 3 months he can have a week off and you can have a few lie ins, in case you have a baby that doesn't sleep. Try to keep early mornings at the week-end free indefinitely. I find even now that I need a lie in at the week-end as I just don't get enough during the week and cumulative sleep deprivation is worse than that you get at the beginning.
Try and think of incentives for your DSs to get ready and out on time (star charts/chocolate after school etc etc). Buy in lots of videos from charity shops for when the going gets tough and you can give them one to keep them quiet while you do the things you need to.
I found about three months in that I just wanted to stay in and cuddle my baby (our last ) and cancelled lots of social things. So, try not to over commit socially.
Even now I keep lunchtime until the school run free for housy stuff and feeding. If you are breastfeeding and have two others, you will probably need to rest a bit to keep your milk up. I also try to get supper started during the day so I am free when DS1 comes home from school (which of course is when new babies also start their mammoth feeding sessions).
Oh yes, make sure to buy your sons' teachers nice Christmas presents so she/he turns a blind eye to any lateness
Good luck, I'm sure you will be fine!