I think you mean global. There is no concept of public/private in Lua. (At least not in the way a C++ or other OOP language uses these terms.)
The answer is yes. Just store the table reference in a global:
\_G.myStuff = {}
Ah, I mentioned composer’s set/getVariable() to, but then saw you mentioned it. I’m pretty sure that should work fine, but if not a global will do the trick.
Note: Globals are not bad. This is why globals exist. However, using them accidentally or needlessly is messy/bad.
PS - Don’t forget you can pass arbitrary data via params in gotoScene() also:
https://docs.coronalabs.com/daily/api/library/composer/gotoScene.html#params-optional