You can certainly drag a book to work and study during your lunch hour. If this is your first time taking the DAT, depending on your level of comfort with the material, I would probably put the volunteer efforts off. If you're taking practice tests and getting into the 20's, then sure, by all means, donate your time a little here and there.
I had a very hectic summer last year, but I did okay because I managed my studying time very well, sneaking in some studying on breaks, and because I'd taken the DAT once before. I already knew where I needed to improve. I wouldn't have volunteered much. I've seen a lot of success from taking time off specifically to study for it, and I'd recommend that over piling on more work.