Let's not judge the poor guy.
He asked if he could use this bike on the track. For this purpose alone, yes, you can. As long as you are only training and then setting a record by riding at speed on the pole, you won't hit a pedal. And your choice of crankarm length -- you still won't hit a pedal.
It's actually not true that the angle is the same at the pole as up higher on the track. This is only true in the middle of the banking. Elsewhere, there's a change in angle of the banking going from the straights into the banking.
The place you will crash on the OP's setup is if you are riding up or down the banking, or riding slowly on the banking. In either case, you are likely to clip a pedal. You want to have a practice of riding at the pole and, when you want to slow down or change position, drop down onto the apron. Still not entirely safe on the apron, but you can figure that one out at low speed early on.
Track power riders traditionally rode 165's. Now they're spread all over from 165's to 172.5's, with 165 and 170 being the most common. Riders who are doing long endurance record rides tend to go to 172.5 or 175 mm cranks. And these generalizations are pretty consistent regardless of rider dimensions.
I would suggest that you spend some time on www.fixedgearfever.com
. This is the hangout for all the serious trackies (and that means many national and world champions, so understand that there's a level of sophistication in the posts once you figure who is real and who throws BS around. You'll find a lot of info about endurance events, crankarm length, almost any track in the world, etc.
Practically speaking, to achieve your goal you will need to do quite a bit of track riding. That means you'll be sharing the track with others and you can't just hog the pole. Accordingly, you'll be riding up and down, riding pacelines with other riders at different heights on the track, etc. etc. Just doing that kind of riding, plus riding with other trackies, means you want to be doing it on another bike with safe pedal clearance, and just switch to your record bike when you are doing dedicated training and the track is closed to everyone else. (You only have to veer up-track and slow down once to avoid another rider to clip your pedal and crash, potentially bringing down other riders. Causing crashes that bring down others is an absolute no-no on the track and you won't get to bring your bike back on that track again.)