If the GSP is currently in freshwater at your retailer, then you can certainly add it to your tank after it has cycled. But, a GSP will live in freshwater for only a limited period, and eventually needs brackish water. Ideally, you want half to full strength seawater (SG 1.010 to 1.018+). A high hardness and alkalinity is important, too.
Converting an established freshwater tank to brackish is tricky, because the freshwater filter bacteria need to adapt to saltwater conditions (or die and be replaced by saltwater bacteria). In practise, you can take the tank up to SG 1.005 within a week or two without any problems, but after that, you need to raise the salinity very slowly, say one "point" on the scale every other week (i.e., 1.005 to 1.006, etc.). At the same time, you need to measure your nitrites. You GSP will cope with this salinity change just fine.
GSPs aren't "hardy" fish in the sense of being tolerant of ammonium and nitrite, so they aren't ideal fish for immature aquaria. If you can, buy or borrow some black mollies to run in your brackish water aquarium for the first 2-4 weeks so you can see that everything is working as it should. Mollies love salty water, and they are indifferent to nitrites and ammonium, making them ideal for this job. When you're done, you can either keep them (risky with a pufferfish) or trade them in.
Oh, and a 12 gallon tank will hold about 0.3 GSPs. A single GSP needs at least 30 gallons (they get to 15 cm), and multiple specimens 50 gallons+. Even a figure-8 puffer, at 8 cm long, would be pushing your luck. With a 12 gallon, the various dwarf Carinotetraodon puffers make much more sense. I have a pair of C. irrubesco in a tank this size along with some cardinal tetras, Otocinclus, and baby halfbeaks. C. irrubesco are funny fish, mine are mild as milk, but some turn out to be very aggressive, so there are no guarantees when it comes to mixing them with each other or other species. Still, they're pretty and the perfect size for your tank. They're freshwater fish, not brackish, which makes your life a bit simpler.
Cheers,
Neale