You are correct. Taprites do have a check valve. Lots of older and cheaper regs do not.
I'm normally a set it and forget it kind of guy but when in a rush I've employed @radagast's method as well as keg rolling. You can overcarb pretty easily by rolling if you're overzealous and have the gas up high. I find 48 hours at 25-30psi, gas off, burp it, then 9-10 and it's generally drinkable but will be fully carbonated at about 2 weeks regardless of the method you use.