I don't really know. I don't suppose I would, but I love new babies, and would probably want to see the baby ASAP. However, I've got 2 DS's, so I'll never have this issue. I don't think however close you are to your MIL, that you would want them there in the same way that you would want your own mum.
My mum was there for the birth of both DS's. Outside the theatre for DS1's ec/s, and in the room holding my head for DS2 Her support both times was fantastic, and I am very pleased that she was there.
In the case of DS1, she lived hours away, but I rang her when I knew things were kicking off, and she was there with hours to spare. With DS2 my waters broke on the Sunday, but he wasn't born until the following Saturday (stop start contractions ended up with induced labour). She managed to get there in plenty of time even though she didn't set off until the Thursday and lived in Cyprus at the time!