Potential new driver.

That depends on your employer and on what schedule the CDL school you use can accomodate.
THERE IS NO TRUCK DRIVER SHORTAGE. There is an oversupply of truck drivers and a lack of freight. The industry is in a recession.

 

Some cdl schools have weekend classes for those that need to keep their regular job while training.

 

What time is your swing shift. If it's late afternoon until midnight, maybe that would work for full time cdl school.
Ask various schools in your area what the hours of the classes are.

 

Another factor would be how far away is the school from either your current job or your home. Say you work the 11pm to 7 am shift, you could possibly attend the day classes from 8 am to 3 pm, if the two are not too far apart. But your lack of sleep after a while will catch up to you.