I started gaining weight on T, but I think what I did gain (at first) was mostly muscle. Not that I'm claiming to have biceps suddenly spring up; but I remember being like 10lbs heavier without my clothes getting tighter. Lifting weights got much easier without much effort on my part. It didn't fluctuate either way after that (not without me intervening anyway)
Then I had surgery, and to answer the second part of your question most of the loose skin on my chest was removed. Around 7lbs came off...not just skin though, the whole lot.
Recovery made me lazy, I've only really just started working out again this past two weeks and gained a good 15lbs over the 6 months I've been sitting on my ass. Which seems to have mostly gone to my stomach, so I guess fat redistribution is kicking in for me because it usually goes to my hips and ass. Unfortunately, my hips and ass were already big to start with, so now I have a big ass, hips and stomach

.... but also a lot more muscle than I've ever had before.
So in a nutshell, for me T seems to increase my ability to build muscle and makes me gain fat in different places; but fat loss hasn't been affected.