A GPS will do very little to help you on the route.
If you have good weather and good conditions, and are a competent, experienced climber then it is possible.
The upper summit ridge is windy and a bit narrow. An uncontrolled slide there would hurt. Many sections of the route between the Tete Rousse and Gouter hut are quite steep with some exposure. You may have ice-slicked rock and be wearing crampons. A fall there would hurt.
Crevasses are generally not a big threat on the Gouter route, but are still a possibility. If you vanish into one and no one sees you go in (or you slide a bit and then go in so you're off the track), you might be in a world of hurt.
WIthout knowing your experience and skill level I am not in a position to say that it's either a good idea or a bad idea.
But I found the route to be a little more challenging, both technically and physically, than I was expecting. Some of the guide websites say, "You need no experience, it's an easy walkup." That leads you to believe that it is a cakewalk. It's true that it is not a technical route, but you'll be using your hands to scramble for a good 2-3 hours, followed by a few hours of glacier/ice/semi-steep snow.
If that's not a place you're comfortable solo (I'm not), then take that into consideration.