I used to wear glasses all the time. When I turned 40 I had the LASIK proceedure, and now I am FREE! Well, sort of. I still need to wear reading glasses, but I can do sports and drive and socialize without the stupid glasses.
As RM_Guy said, the biggest problem with wearing goggles over the glasses is fogging. The goggles have a small tendency to fog up, but the glasses underneath are even worse. The worst situation is when both the goggles and the glasses have fogged up.
Back when I wore glasses I also did a lot of scuba diving. There are not any dive masks that you can wear over glasses. There were masks that had lenses available in the standard diopter corrections but that didn't work for me due to my astigmatism. Then I found that I could get a special set of lenses made that could be simply glued into the mask. Problem solved!
Note that the lenses were special, they were not just an old pair of glasses glued into the mask. Unlike regular lenses, which are curved on both side, the special lenses were flat on one side and had all the correction on the other. The flat surface glued down tight to the mask glass and had no air gap.
I would certainly try a pair of standard goggles that are made to fit over glasses. If it works for you then there isn't any problem. If the fogging or fit causes you problems then I would save up for a pair of those Pro-Vue goggles. Or ask your eye doctor.
Rod