It is totally possible to get some pretty nice results using the stock GoPro. We always recommend using a modified lens, such as the one we sell on DronesMadeEasy.com, but it is possible without it if care is taken.
Be sure the use the narrowest field of view setting (lowest resolution) and have plenty of overlap. Flying at around 125ft at 8mph while taking images every 3 sec seems to be working well for people.
Since the GoPro doesn't record geotags in its images, you can use our online georeferencing interface to define anchor points in your images and on existing basemaps (e.g. Google Maps) to align your map with the world and use it as an overlay.
We recommend using whatever you have to try the system out and see what you can do with it but keeping in mind that things get better when you use a flattened lens or higher quality camera. We continue to be impressed with some of the maps people have been making.
I hope that helps.