IIRC there is no conditioning work built into it. If you do prowler work with even mediocre intensity, I suspect you'll have difficulty hitting reps. If you have comparatively high bodyfat (15-20+%) 30-45 minute fast-paced walks in the AM, on an empty stomach will be plenty of conditioning if doing TTM properly.
I would also recommend sticking to going for 5RM's instead of playing with maxes between 1 and 4 reps. Maybe once you're more advanced, but most people thinking about TTM that haven't started it are not that advanced.
The only variation I would make--one that MR described in his article 4 months ago--is doing DE deadlifts on Friday instead of olympic lifts. If they work for you, fine, but if you want to compete in powerlifting, I think you'll get more out of DE deadlifts vs. PC's.
Also you may already realize this, but the program is written as Bench/Press/Bench, M/W/F one week and Press/Bench/Press, M/W/F the next week.
You should do it--it's a good program, but anything I could tell you is less valuable that what Rip has already said/written about it