Can I compare DFT calculations with different grids?
Yes, your error analysis is valid for energy differences. However, I believe it is also valid for the absolute error $\epsilon_i$ of any calculated quantity, not just the error $\Delta\epsilon$ of an energy difference.

In any numerical computation, the key thing for situations like this is to ensure that these "structural" sources of error have been reduced to a magnitude that don't affect your results. In this case, this is achieved when you reach a grid quality $Q$ where the numerical results no longer change when you further increase to $Q+\delta Q$.

To be clear: in this case elimination of the imaginary frequencies is not a good criterion for a sufficiently large $Q$.  The proper stopping point for refinement of $Q$ is when the results no longer change appreciably.

Note that, as you allude to implicitly in the question, this situation is different than the one of trying to compare, e.g., absolute energies from computations run with different methods or at different levels of theory.  In this case, there are fundamental/theoretical reasons why those comparisons cannot be meaningfully made.