It's hard for any of us to give you a definite yes or no answer, since hormones effect everyone slightly different. Some people experience particular changes while others don't. However, most people who go on T don't seem to report any height difference, unless they're still in puberty, sometimes the T can jog your body into giving you a couple extra inches. But if you're not going on it for a few years, it's likely that you won't grow much taller. I have your same problem though, while I'm two inches taller than you, I'm not happy with my height - since I'm shorter than most of the men that I know, so to give myself two or three more inches, I stuff my shoes with paper - it's a little uncomfortable, and lifts would be better, but it's cheap and it works...until I take my shoes off.