It's most certainly something you can do. The real question is "how" you would accomplish that.
When your gun picks something up, that something would need to be converted from whatever it starts as (presumably a unit) into a missile to "launch" to the gun, and then converted to a model attachment on the unit holding the gun (with a bit of an offset so it's "hovering" in front of you. bonus points if you get it to wobble a bit independent of the unit "holding" it).
You'd then have to be able to convert it back into a missile to "fire" it off, and then finally into whatever state you want it to go into when it lands (destroyed? back into a unit you can pick up? etc). You would also need abilities to control the pickup/fire behavior and any necessary supporting triggers.
I think you could do this without the missile conversion step as well if that's easier for you - but you'd then have to do all the physics stuff in triggers and you'd still need to convert to an attachment and back.
Do you want to do that with the new Physics stuff?
It is probably possible to do it from a purely visual standpoint with that, but right now it is uncertain if that system can have an effect on other actors (that are not ragdolls) so you can check if the object fired with your gravity gun hit another actor/unit and is supposed to do damage, how much etc.. I think it is purely actor based, so you probably can't do all that stuff and it is purely visual.
I mean a key feature of something like a gravity gun is in my opinion that the projectile fired from it is an actual ballistic thing that has different impact on the target depending on the speed on impact, the mass of the projectile, the mass of the object and the material the object is made of. I don't think SC2 has inbuilt data that support these things right now, so your best bet would be to use triggers for the whole system in my opinion (maybe except for the gravity gun itself, but I don't know. There are certainly things you can do with data regarding it). If you don't care that much about the real physics behind it (like faster projectiles doing more damage, light projectiles doing no damage at all etc.) the missile system should be good.