The carpet is stapled down underneath everything. It was put down when it was a bare flatbed trailer. So you'll have to cut at the edge of the walls and cabinets.
There's also a ton of staples in it, so you'd have a large amount of staple holes, like by the area just inside the door where it transitions from that small piece of linoleum to carpet. You also have two pieces of flooring in the trailer, most likely one in the front in the kitchen area over top of the main piece, and that should extend probably back to just past the bathroom.
So the answer is yes, you could take up the carpet, but you would probably have to put a few random edge strips in to cover the staple holes and the linoleum seam probably in the bedroom.
2007 T-286SR Cherry/Granola, #6236, original owner, current mileage: 9467.8 (as of 5/26/19)
1997 T-2653 Blue Denim, #5471
1979 12 1/2' MC, Beige & Avocado, #4639
Past Sunlines: '97 T-2653 #5089, '94 T-2251, '86 T-1550, '94 T-2363, '98 T-270SR