this is definetly possible. i went from level 250 to level 264 (almost 265) in about 4 days of hardcore grinding.
i usually grind about 8-10m exp a day ( i get 65535 exp per match and the match usually is under 2 mins. some are around 1:10).
10 mil exp = 153 games = roughly 5 hours of grinding = 306 mins (at a rate of 2 mins per game but like i said alot of my games is with calvin and there around 1:10-1:20)
So technically grind for 5 hours each day for 13 days on 258 hard would = 113m exp. so technically you could do this in 13 days. but lets say he had enough exp for lvl 240. he could have got 270 in like a week. Not all no lifers are hackers :3