Does modelsim_ae 15.1 support sparse memories?

From my understanding, in any simulator, declaring a memory like you did will always require the full area to allocated. Your error message seems to indicate it is struggling to allocate 16mb, which may indicate a system problem?

The memory you describe is not very large and shouldnt require much system memory.

A sparse memory would have to be simulated with something like an associative array as you suggest, but this is not synthesisable. This would mean you would swap out your synthesisable code with your sparse memory model. But for such a small ram, I would never use such a thing as it is so small (when you start talking about DDRs, then you should think about sparse modelling).