Yes, it depends on the home range, excluding very long excursions to different habitats :)

If you haven't seen it already, this paper may be useful for you: http://onlinelibrary.wiley.com/doi/10.1111/j.1365-2664.2009.01710.x/full

They used species presence/absence reports from wildlife experts.

Average home range size of an animals may be use

Ths paper indicates what happens to your results if the grid cell size is to small or to large:

Article Occupancy in continuous habitat