Virtues of Mixing a Mono Track

Comes down to how the human auditory system perceives and parses audio. That system is quite sophisticated, but all the sophistication is in your brain, not in your ears, and the brain can only process what it's handed. Your ability to differentiate between components in a mix depends solely on the only three factors your bio-hardware can report: amplitude, frequency and phase. Consequently, those are the only things we can work with in a mix in order to manipulate how the listener perceives it.
 
Take away stereo perception and you take away 33% of those variables, leaving only amplitude and frequency. It's a smaller palette, but think about what Picasso did with a limited palette. Lacking color contrast, he focused on the other elements to make compelling paintings. 

The point being that by concentrating your efforts on a smaller subset of variables, you make them more effective. This is where the concept of "if it sounds good in mono, it'll only sound better in stereo" comes from. All the things you do in mono are applicable to the stereo mix, even if the converse isn't necessarily true. 
 
Which is a longwinded way of answering your question regarding whether EQ should be tweaked specifically for mono. Most of the time, the answer is "no". If an EQ change helps the mono mix, it will probably also help your stereo mix. 
 
I say "probably" because there could be situations where the frequency spectrum can become unpleasantly unbalanced in stereo. For example, say you have a major component that lacks highs and is panned left, and another major component that's all highs and it's panned right. Now you have an uncomfortable imbalance that'll drive listeners nuts on headphones, but hadn't been a problem in mono. But that's not an EQ problem, it's a panning problem. Or perhaps an arrangement problem - maybe that tuba and piccolo duet wasn't such a great idea.
 
Sorry for the ramble. The caffeine is just starting to kick in this morning...
 
 

Some people do just that. I believe Craig Anderton is one of them.

So what I do, and its based on what other mixers say they do, is this:
Get a basic static mix in stereo - kind of a "gut mix", no plug-ins just faders and pan knobs
Switch to mono and use EQ and compression to get better definition of each instrument (if I am going to use mix buss processing I add it at this point).
Switch back to stereo to add effects and automation and then address "problems"
 
I will do mono checks after I switch back to stereo.
 
The theory is that a good sounding mix in mono will sound even better when its put back into stereo (and that has been my experience.)