Is it possible to have an Apple Genius replace my Fusion drive with an SSD in my iMac?
Yes and no. 

If it's under warranty, then it's a definite no, even if you're willing to pay for it.

If it's not under warranty, the answer gets a little more complicated because it depends on the exact model of iMac, its status (i.e. is it considered by Apple to be vintage or obsolete), and to some degree to your location.

The best answer we can give here is that you need to contact your nearest Apple Store and ask them.

My advice would be that if it is under warranty, to just leave things as they are. If it's a real issue for you, then you may have other options (such as using an external SSD as your boot drive, etc).