Can a TPU (Reserve Soldier) who is currently in a non-pay status attend Annual Training before they go to BCT/AIT?

Army Regulation 135–200 and AR 140-1 cover annual training. AR 601-210 covers enlistments.
AR 140-1, 3-20 "e. Soldiers awaiting IADT, whether in pay or nonpay status, will be excused from AT if the criteria set forth in the above are met. Alternate training enlistees who have completed Phase I of IADT may attend AT, at the discretion of the unit commander.
Prior to basic training, they are still civilians. I understand they are on the roster and can receive pay for attendance but there are specific things that they cannot be faulted for like failing a APFT (you can't flag them because they aren't Soldiers yet), weapons training, or unexcused absence.
The reason for limiting pre-basic participation is because something could happen (an accident or injury) that could prevent them from shipping or possibly exclude them from future service.

You have to go to AIT before you can attend AT. It's a liability issue for the Commander.

SOURCE: No idea on the reg. I'm Active Duty attached to a Reserve OC/T Battalion, so I've been forced to learn a lot of Reserve'isms.