First of all, yes you can, under the strict conditions for instance of the GPS approach. Subject to your CAA and airlines approval of course. However, since I am as hesitant as anyone else to the idea to fly down to minima based on GPS alone I will not use that argument.
edit And of course, the database has to be scrutinized and validated by the airline and the pilots, the GPS constellation has to be check for every approach, you need 2 GPS receivers, two FMGC's etc. etc., all things that don't apply on a standard flight that we are discussing, where there is an absolute need to monitor raw data under the circumstances already mentioned.
Please read what I have been writing. In the cruise, above MSA, there is no need to monitor raw data as long as you have GPS primary. That is what Airbus says. That is what my company says. That is what I follow. Below MSA is a different story, albeit no so different according to paragraph 1.
Regards, you will never see me free-tuning during departure!