Yes, you can book yourself a positive space seat to/from home during breaks in training of 48 hrs or greater. I was quite lucky and had a very gentlemanly M-F or Su-Th schedule during training with a 2 (once 3) day break in between each series of sims, so I did go home 3 of the 4 weekends. I would say that almost all of the guys/gals I went through training with went home at least once or twice during their "weekends", and several went home for every break.

Alot will depend on your sim schedule. I usually had a morning sim so was able to catch an afternoon flight home each time and come back to ATL the night before my next event. If you are on a late aftn or evening sim schedule, then getting home the same day likely won't work and you'd have to decide if it is worth your time/effort to wait until morning and turn right back around the next day to get back to ATL.

The IOE schedulers will schedule your first one or two IOE rotations usually towards the end of your 3rd or start of your 4th week of sims. I had a 5 day break after my last sim and then did a four day and two three day rotations with 3-4 days off in between each rotation. The IOE schedule will vary depending on Line Check Airman availability and you might find yourself doing an IOE flight out of base because of that.

I finished IOE towards the end of a bid month, but if you finish earlier in the month you can request that schedules builds you a line of open time for the remainder of the month, otherwise you will likely receive a partial reserve line until the following bid month.