Yes, you are correct- the bouquets themselves are not "magical"- they don't do anything on their own. They are props that are meant to be produced or pulled out of the sleeve. The "magic" part is that the flowers can compress into a narrow space, like your sleeve, but immediately fluff open to appear very big.
Yes, this takes no practice on the part of an actor. All he has to do is pull the stem out of his sleeve, and out comes the bouquet!
If you need more suggestions for tricks that will fit your situation, please call Peter Monticup at 540-832-0900 weekdays. He's the owner of MagicTricks.com, and he is always happy to help.