As far as players interacting with a square grid for the first time, this is an interesting case. I think that when the players are first interacting with it, it might seem like a different enough situation to not seem strange. The players would be building their first structures or buildings from the perspective of a single creature, and would be done in very small amounts at first, just a single shelter or building at a time. If the buildings are square/quadrilateral like a player might expect them to be (the society center in the prototype society stage is already quadrilateral…) then the square grid would probably feel natural. Of course, if it actually turns out that way, we will have to see (or do more research first).
To tie this discussion in to the world generator that I proposed, DGGIS (The World Generator: A Dynamically Generated GIS), I am envisioning that a tiling would be more apparent only near the ‘base unit’ of the tiling (the lowest possible LOD level). This base unit for buildings could be a more constrained tiling like Sim City 4, where each tile could be an entire building. Or it could be a smaller unit which the buildings are aligned to, but are not as coarse as entire building sizes. Once the perspective shifts to higher scales, like in the later society stage and industrial stage, then the grid would become much less apparent. The cities would not just turn into large squares representing an entire city; they would just become lower resolution approximations of it. With a good LOD system the approximations should be unnoticeable, and the grand strategy view you would have of your World would not use large hexes or squares, but would appear continuous. (Until you zoom back into the highest LOD level, where the individual buildings are constrained to the grid). This would result in the large scale strategy view appearing to be like a free form placement, while the small scale regions would be constrained to a grid. However, as stated in the World Generator thread, I don’t think that doing it this way is a requirement of the design, only one that I think could give good results.