I think it's the greatest idea I have ever read on these forums. Kids are very protective of their Mom and I don't know where their father is but they will fear losing the Mom once the "new guy arrives" in your life.
By him living with your Mom for a while it will give the girls time to know him and get used to him rather than him move in all at once.
The 13 year old will be going through a hard enough time with teen issues coming up and hormone changes so as a divorced women with kids I totally understand and absolutely admire you for putting them first.
Good luck
And have a good talk to him that you will be the only one to disciple the girls when they do wrong or again they will resent the "new guy" telling them what to do.