Ok, we've established that the fish is not reef safe, so now let's discuss it.
I've kept "non-reef safe" (NRS) fish in my tanks before, and will do it again, but there are important trade-offs you have to consider when you do so.
Most NRS fish will attack inverts, and some will attack corals. I've had eels and NRS wrasses in tanks, and they would go after my cleanup crew regularly. The solution to this was keeping them well fed, and replacing the cleanup crew more frequently. I enjoyed the fish, and didn't mind the added expense. If a fish likes to munch a specific type of coral, you have to either lose the coral or lose the fish. Your choice.
In keeping them well fed, you run the risk of fouling your tank water quickly. Most of these big eaters add a heavy bioload to the tank. I think the biggest issue you'll face with the puffer is keeping your water quality high.
Can it be done and should it be done are different things. If you're prepared to lose your cleanup crew (probably your shrimp), and potentially some corals, then you'll just have to worry about the added waste in the tank.
All of this said, I would probably advise against it, unless you have the time and money to do frequent water changes and regularly replace your losses. If you had a larger tank, I would say go for it, but in that size tank, I think you're going to have more trouble than it's worth.