From experience with other engines: essentially, yes.
If I check the box that makes a Material ‘Two-Sided’, does this mean that every object that uses this Material becomes twice the poly count? Thanks in advance.
Well, yea pretty much, although there is still culling when not visible by camera so I would say that it only really counts for complex objects/ bended objects where you can see both sides at the same time.
Ticking Two-Sided Checkbox is not the same as duplicating and inverting faces on the mesh. Briefly, the vertex count will remain the same, pixel shader will run twice.