I agree that a 2 PSI (if it is or isn't valid for these motors) shouldn't a problem. After all, 2 PSI is equivalent to the pressure of over 4 feet of water column and over 5 feet of gasoline. If you assume that half of this head would allow the fuel pump to push/pull enough gas to keep the engine running, you're still looking at two and a half feet...
As far as some carbs having a spring, and some not, if the diaphram is 'springier' it could be act as it's own 'spring.' Or, if the carb was intended for use on a motor with an attached fuel tank, the diaphram could be springy enough to work just fine...
However, the physics of the design of a separate diaphram-style fuel pump are exactly the same as an attached fuel pump. The basic pump design is the same as well. (Specifics, of course, can be different.) So, in that regard, the information provided by Walbro describing how separate diaphram fuel pumps actually work is applicable.