I played when I was really young only a handful of times and I was absolutely terrible, never took scores. I gave up until I took the game up fall of 2012 at which point I started to keep score and actually play by the rules. At that point I was playing a cheap 150 dollar set from amazon, probably averaged 110 strokes+ per game. Last summer I bought a boxed set of Adams tight lies and really started to play and enjoy the game. I played 1-2 times a week and went to the range at least once. I started recording my swing and watching tons of videos (I am 21 now btw), this allowed me to learn pretty quick. I started last season shooting that 110 that I ended on in 2012, and I finished out last season averaging low-mid 90's. My best score last season was roughly bogey golf 88 (playing 9 holes, scaled to 18). My first round this season a few weeks ago playing that first first round with my new custom fit irons, I shot 36 on a tough par 3. Granted I had been to the range 4 times before I played.
I really hope this is a good sign for the season(s) to come my goal is to get down to 80 this season. So to answer your question, yes you can definitely get better. The key is to become a student of the game. Watch the golf channel, perfect your swing, watch instructional videos, get fit to some clubs once you get a consistent swing down! Playing pretty good golf should be completely possible for you.