I know that in vanilla minecraft you're practically guaranteed to get more materials than you use while branch mining. Is this still true in the TerraFirmaCraft mod or is using the prospector's pick necessary in order to have a net positive return?
No, it is not.
In vanilla minecraft, branch mining works, because all resources are generated in small chunks evenly distributed in space. So to get most of them, you need to uncover lots of space.
In TFC, the ores are generated in huge chunks far away each other. So even if you uncovered lots of space, you get minimal resources. Prospector's pick comes into play here, because it allows you to get basic idea if there is any ore in ~20 block area around you. This way, you should make branches ~20 blocks away each other. Not 2-3 blocks between.
Simply said, getting first reading on prospector's pick is the hardest part. Getting to the ore after that is relatively easy. If something like PP existed in vanilla MC, you would be getting readings all the time, so it would be practically useless.