It will work fine, except you wont be able to limit mac addresses on the unmanaged switch on a per-port basis. You'll be able to limit the amount of mac addresses allowed on the port of the Cisco switch the unmanaged switch plugs into. For example, if its a 12 port unmanaged switch and it plugs into port 3 on the cisco, you can limit the amount of mac addresses allowed on port 3 to 12. Which could equal one per port on the unmanaged switch, or if you have another switch plugged into that, it could mean 12 mac's on one port of the unmanaged switch. Make sense?
As for 802.1x, that requires some sort of authenitcation server, usually RADIUS...and the price of that software can get kind of expensive. MAC-based port security and 802.1x compliment each other, and 802.1x is probably the more secure and adaptive of the two...but in the end it's probably going to be more expensive.