If the stock WAS NOT collapsible then yes it will fit right just as you can take a 1100 factory stock and put it on a 870 and vice versa. Since the stock you are wanting is a collapsible then none of the above applies. The 1100 has a tube that protrudes into the stock for the action spring and this makes the collapsible stock a no go.
Here's a cut-away showing the internal structure of an 870/1100 stock. The 1100 has its recoil spring where the bolt is on the 1100, so unless you do a Sidewinder conversion, you'll have that to contend with.