There's more to mics than EQ, though.
Transient response, polar pattern as Boz mentioned, distortion (very minor in most cases but our ears are pretty sensitive), proximity effect, resonance, phase shifts, and all of these may vary at different volumes, frequencies, and angle on/off axis.
EQ effects introduce their own phase shifts, resonances and distortions too. So mangling one mic to sound like another will introduce these extra distortions.
Then there's the practical considerations - a ribbon might blow if you put it near a kick drum, a C414 is quite expensive to put within stick bashing distance of a drummer, an SM57 might sound boring with a particular preamp because the input impedance doesn't suit it, A U87 might push a nice preamp into subtle overdrive where an RE20 won't...
How much all the above matters just depends on the particular situation you're in and what you're recording. But to directly answer your question, let me give this extreme example;
An SM57 will never sound like a typical condensor mic, because the diaphragm doesn't move as fast - that's detail which is lost and will never be returned by a HF boost.