What you are describing is 'amp and speaker modeling' (which would be the electronic correlate to close mic'ing a cab through a PA). That involves quite a bit more than EQ, but can be done, especially given that the traditionally horrible sounding modeling software/hardware is getting better by the month.
Also, remember that most well designed PA"s have subs, true midrange sections, and then upper midrange/treble boxes, expertly crossed over (usually electronically). That is different than putting a driver designed for subwoofer applications into a relatively small, higher tuned box, and then adding a small mid driver to cover the top end. Quite a different thing there. Again, not a 'good versus bad' thing at all, just a 'different thing'.
Much easier to get a rig that sounds like you want it to sound IMO and IME