I believe that thermorest recommends storing for long periods in the inflated condition rather than rolled up tight. I have a pair of thermorests with the valve open behind the living room couch, leaning against the wall. They cannot be seen without really looking for them. I have a pair of cheaper (and thicker & heavier!) Coleman self inflatables from Sam's Club. The instructions that came with them recommend inflating prior to use, then rolling them down and inflating again to restore loft. That seems to help with those mattresses.

I would think that if you are in a training program, that leaving them rolled for a couple of months shouldn't cause any permanent issues.

When we went training with the Scouts for Philmont, I packed my pack about 70% with what I was going to bring on the real trip and made up the rest of my desired training weight with water bottles. Easy to adjust prior to leaving on a practice hike and if you find out you bit off more than you can chew, it is easy to shed those pounds so that you can make it back before anyone starts getting worried.

It would be worthwhile to carry the thermorest a few times to get the feel of it. They have a tendency to stick out farther to each side than you expect. But you don't need to carry it everytime. Make up the weight with something else.

Something to consider. I had a new internal frame pack for my trip. The top of the pack had a detachable fanny pack as the cover. The thermorest went under that fanny pack. Found out the hard way on the trail that the rain cover for the pack was spread wide at the top by the thermorest. With the wind in the right direction, the rain collected and puddled in the bottom of the rain cover. Wet sleeping bag. I thought the rain cover would eliminate the need for using a garbage bag for waterproofing around the sleeping bag. Needed just a couple more inches of material to each side of the rain cover. I would recommend trying out any rain cover you might use with the thermorest attached to your pack prior to making your trip.