I just finished with an instrument student who owns an airplane equipped like that. Actually, he has DME as well.
While the training went fine, we were noticeably limited in the approaches we could fly that were available locally. Without DME, he would have been even more limited. Especially as the FAA cancelled a bunch of VOR approaches earlier this year, you may notice yourself flying the same approaches again and again unless you extend your lessons farther and farther away from your home field (not a bad idea, of course, but does tend to lengthen the lessons).
Basically, it's becoming harder in many areas of the country to train effectively with only VOR/ILS. (By effectively, I mean having access to many different approaches at many different airports reasonably nearby.)