You're going to have really big performance problems if you have a gigabit WAN conection; a gigabit Internet service, but a mesely 10/100 router in front of that. That will cut your Internet surfing performance right down.
But otherwise, what of the communication to the router really needs to go at gigabit speed? Allocating an IP address via DHCP? These things run just fine at 10/100. It's only the local computer to computer transfers that can really run at gigabit speed, and those will go directly from the switch port to the other switch port, without having to make a round-trip through the router.
So short answer -- it'll work just fine.