It can be done! (and even with old monochrome version!!)
As the airplane I picked up had no installed GPS (yes, there still are a few), I took two handhelds along. The photo was simply for my own future amusement, that I had a C 182 going 179 MPH at 12,700 feet (it had actually peaked at 181, but I missed it).
When used in harmony with a chart, it was completely satisfactory, and far superior to the dead reconing, with perhaps one VOR, of my earlier days of flying.
It was interesting later in that flight though, as I crossed the rather featureless expanses of central Saskatchewan, that neither GPS would obtain a useable signal for nearly an hour. With no VOR's within reception range, I did have to revert to very basic (and much less precise) navigation for a while. I am convinced that even a panel mounted GPS would have suffered too, as both of the handhelds showed unuseable constellations for that period. This was not the only time this had happened to me, though is was the longest period.
Even a modest GPS, operated appropriately, is a wonderful supplement to a chart, and safe navigation.