Used to be but they FCIF'd that away a decade ago.
Not to sound snarky, but with what you will be making at FedEx you don't have to make yourself completely miserable. A shared crashpad room can be found for 200ish, a private one for 400ish, and in some good neighborhoods.
As a technique, when I was there in years past I kept a car, but would float from hotel to hotel. Weekdays were often spend 40 minutes away in Tunica casinos, which had 24/7 food, good gyms, and a nice pool in the summer. The Grand/Harrahs was closest but went under, but there are still bargains to be found Sunday-Thursday.
Weekends I would migrate to Millington NAS. World class gym (Dugger center), great outdoor pool in the summer, and safe place to run and be outdoors.
As I got more senior and didn't have to watch the $$$ as close, I often just stayed at Marriott Courtyard close by. Once I ditched MEM car a few years back this was nice.
There are some nice RV parks in MS, and a good friend stayed out at Shelby Farms for training in an RV park. I think hanging out on Sardis Lake might be a nice respite from training, and the training center is easy to get to off of the interstate (assuming you aren't training at Hack's).
Everyone has a different way of dealing with commuting, and I understand as a new hire you aren't loaded. However, I will say that one of the smartest decisions I made was deciding "it wasn't going to suck..." when I went to work. Take care of yourself, make going to work as much fun as possible (and there is/are some fun things around Memphis) and enjoy it. Picking up one trip a month will more than cover the difference in cost, and lately there's been a ton of flying available again.
Probably more than you wanted than just a simple "no" but I hear some of these questions frequently.