If I had a very young (under 2) toddler/baby, I probably wouldn't. Older than that, I probably would. Our DD had just turned 2 when her brother was born, and he was born during her naptime. We woke her a few minutes after his birth to come and see the baby still attached to the cord, the birth pool, all our family who had gathered there. We have the sweetest picture of her half asleep and slightly confused little face meeting her baby sibling. But she was/is a very mature kid and I have no regrets about getting her out of bed. After the birth she seemed no longer in need of a nap and got to be present for the newborn exam and first nursing sessions, etc. I am really glad she was there for all that.
This time around she's 5 and VERY excited about the birth, and very worried she'll miss it! We will definitely wake her up if it happens at night. I am so excited to have her involved with the process of it all! (Well we wouldn't wake her in early labour, but once pushing started then we'd definitely get her in there).
DS is 3 and knows the baby will come out of my belly. I think we'll wake him too. It would be odd to have the whole family there except him. I feel very drawn towards having our whole family as involved as possible through the process of the birth. Not so much the labour, but the birth and immediate moments afterwards. And he is the type of kid who will tell us if he would rather go back to bed! If he doesn't want to stay awake he will certainly be welcome to go back to sleep in his bed.
Hopefully this will all be a moot point as both my kids were born around 2 pm. :)