Yes, I'm sure because you can go to almost any garage and you will find a Varsol station. You will often find dirty Varsol being stored in 5 gallon buckets that used to have engine or transmission oil in them.
Since it is used as a cleaner it is common for people to cut a 5 gallon pail in half and fill it with solvent to clean very dirty engine parts. This is often left out for a long period of time, and if you keep using the same container for cleaning it "changes" and becomes softer and more pliable than before. But I've never seen it get eaten up, a container that had a hole eaten through it or something like that.
Another story, the machine I was using was a thread cleaner for large industrial pipes and it used Varsol. I would make a splash guard out of a used HDPE bucket with the top and bottom cut out. After a long time the splash guard really does change from being exposed to varsol all the time. It becomes very soft and curls... but again based just on visual inspection there was no plastic being eaten away.
This was all at room temperature by the way.
I remember the ingredients on the MSDS were xylene, toluene and mineral spirits. You could be right that the original container was a special blend of plastic.