I can't say for UT but I can for Quake 3 on PC. It takes a lot of playing and you will eventually get to your potential. But do not confuse this with meaning you can become a master at a particular game. Some games will be better to do that for than others. When I had hit my peak on Quake 3 I was not a master of the game. I could beat all levels on Hardcore and all but 3 or 4 on Nightmare. As far as multiplayer goes, I would say I was in the top 2% of players that I faced. I would win every match except when playing against the few that were better than me.
I played in one Q3 tournment that went for 8 hours or something and I ended up in 2nd place when it was all said and done. It looks like that host's forums are now gone but it was hosted on the vogon.vg server which ran an extra fast/excessive type mod.
As far as other types of tournaments, I've only won local pinball tournaments, and done decent at tournaments with top ranked players. I could probably get into the top 1,000 if I travelled out of my area.