It does, in my mind. To explain what I mean, back in the late nineties/early 2000s there was a small miniseries of Star Trek books called The Captain's Table. Long stories short it was mostly an excuse for the various captains to tell stories in first person, but essentially The Captain's Table was a bar that could be accessed from anywhere in any time(During Picard's book, for example, there was at least one 1860s sea captain listening in to his story.) The bar also seemed to change appearance depending upon who was viewing it.
I propose The Inventory works the same way. Let's look at the facts. Firstly, Tycho's world in Penny Arcade has never shown any indication that it takes place in a reality very far removed from our own(besides a couple of robots.) More to the point he's aware of the existence of Max's video game series and the Heavy's, which even the Heavy doesn't seem to be aware of.
Max's universe is shockingly different from both our own and presumably the others as well, with the most important difference being Max as President. Because of the sheer number of sentient species other than humans in Sam and Max, and because there has never been a sign of such in Penny Arcade, at the very least these two cannot coexist in the same reality.
Strong Bad is an odd case. His whole town is bizarrely animated, with even the supposed relatives of each other looking so incredibly different from one another that something odd is going on with biology there. Plus with nothing ever being acknowledged outside of Free Country, USA besides the e-mails, it seems to me that it would be very hard for Strong Bad to coexist with any but Max, and even there it's debatable.
The Heavy is the best example. His whole game originally took place in a late 60s environment and while he's been updated to the 80s in his references, the fact that he's recently gotten a "new Walkman" and thinks Purple Rain is new says he's from a different time than the others, and probably a different reality to boot due to the various technologies present.
The benefit to the Inventory existing in this form means that any characters can show up without there being some sort of contradiction or invocation of their existing with one another. I mean we all know there's no way Marty or Doc could live in the same world as Sam and Max, for example. Plus it adds a nice mysterious air to the whole place, one that works to its benefit.