Can an LTM be connected to a Cisco FEX (fabric extender)?

Right. That's just BPDU's. Don't do STP (Active or pass-through) and you'll be fine. (i.e. Don't bridge any interfaces via the BigIP).

You also can't do layer3 interfaces on a FEX port IIRC.

This really just means your BigIP has to act like a host, rather than a separate switch. Which isn't usually a problem... At least the way I like to use them anyway.

H