If I am TDY en route to 91M AIT to reclassify, will I do my PCS leave packet at AIT?

You should have a DA 31 taking you from your old unit, through your school date, and through the time you want to report. The following should be In the special remarks:
(Date you leave loosing command through the day before you report to school, (12 April 2019 - 25 April 2019 (Leave) School report date-School end date (26 April 2019-21 May 2019 (TDY), Start date after graduation date through leave end date or report date (22 May 2019 - 10 June 2019 (Leave) (which ever date you will sign into the unit).
Your from and to dates will be 12 April 2019 - 10 June. The number of days will be 60, however, you won’t get charged the TDY dates or travel dates, this is why you’re going to put the above example of remarks in the remarks section because it explain the breakdown of your travel from the departure date from your last unit, your TDY dates, and your leave enroute to your gaining command.
I hope this helps....

You are supposed to do your leave prior to leaving your unit.
If you are returning to your home station to clear because of your family, you will submit your leave then. If you are clearing your unit prior to AIT then you should get a leave form prior to leaving. Schools tend to act weird about signing leave forms for TDY enroute soldiers.

You don't have to take 31 days of leave. You are authorized to report up to 30 days early. You are given all that extra time to take leave if you choose to because there is not time to prior to attending AIT.