Tow Travel Trailer with Truck Gate Open? Anyone done this?

Before you buy the TT hook up and drop the gate and see how close it is. Without any other info, no you can't be hooked up with tailgate down.

Edit (add) they do sell bike/quad racks that will allow you to put the the bikes vertical to the truck, that is a alternative I have seen.
Example; http://ffcustoms.com/truck-boss-sledatvutv-decks/ and http://www.diamondbackcovers.com/atv-carrier/