I started my toddler in preschool a few months after our twins were born. She was a month before turning 3 when she started. I'm very glad I didn't start her before the twins were born. In the last few weeks before the birth, I would have been completely unable to handle transporting her there and back. Also, in the first few weeks after the birth, I also would have struggled with getting her there-- it would have locked us into a fixed start time in the morning, and when I'm caring for three LOs all night, I need all the sleep I can get-- I wouldn't want to HAVE to get up at 8, to get a kid to school, if I had any choice in the matter. She would have missed too many days. Also, while having her home during that whole time presented plenty of challenges, it also gave her a chance to feel fully part of her newly altered family, and in the long run I think that turned out to be valuable.
There's also the issue of illnesses. Kids bring home a LOT of illnesses, in the first few months of preschool. And that can be hard to deal with, when you're already dealing with pregnancy and birth and the demands of new babies.
I AM however very glad that I started her soon after the twins were born. (They were four months old.) It gave her the chance to feel like the special one, with all the fuss of new backback and new lunchbox and new shoes and all that little stuff that small children get excited about-- and all the taking of pictures, and new friends, and stuff like that. It put her back in the spotlight, which she needed badly. Plus, it gave her some relief from the dreary routine of nursing/diapers/naps that we were living in at home, and it gave me some time to spend with the new arrivals without the constant chatter of an active toddler in my ear the whole time. The twins were old enough to handle exposure to colds and stomach bugs, and I was settled into my new life enough that I could handle a sick kid when necessary. (and it WAS necessary!)