Yes.
Connecting to a non-active claw used to be a good way to summon the Kraken, but I think that doesn't happen anymore. At any rate I've done such a docking once in my current career and nothing horrible happened.
PS. And even if it did summon the Kraken, in the scenario you described you could work around that by switching vessels to the refueling station (with the claw) right before they connect up.
Docking ports of different sizes don't work together. You can connect them in the VAB and they will be able to decouple, but you won't be able to reconnect them in flight once separated unless they were the same size.
In fact you can connect any part to a docking port in the VAB like this and have it decouple in flight, which can be useful (for instance) for putting a launch escape system on top of a capsule. The LES can be jettisoned by decoupling the docking port using an action group, removing the need for an additional decoupler.
Hotaru's post in Docking on an armed Claw was marked as the answer