No, you do not have to put an external wastegate on all turbo. Like TGBol said, the housing are sized to keep from over spooling the turbo. None of the first gen trucks came with a wastegate. Dodge/Cumminns, in an attempt to eliminate turbo lag, put smaller exhaust housings on the second gen trucks and these had waste gates to prevent overspooling.
I have a modified HX-35 on my 93 with a nonwastegated 16 housing. I'm running about 35 PSI boost. Boost is also controlled with fuel so that is a way to also control the turbos. If I were to install a 12 housing, it would probably have to be wastegated to control things. The smaller the exhaust housing, the faster the turbo will build boost. This is not even addressing the compressor housing guys so don't beat me up too bad!