Abed can still win with 5 hero counters against his meepo but he'll obviously have somewhat a hard time. Probably around 6 deaths max with 20+ kills. 
I think Miracle- spammed Slark mostly when he was grinding so obviously they'll gain MMR
If they could only play one hero it would probably drop. As for your related question, it would drop even faster, especially if it was a hero easily counterpicked, e.g. Wraith King, Sniper, Skywrath Mage. If an 8K player only were able to one hero, and assuming that hero had counters but not obvious hard ones, they'd probably drop to 6.5 or 7.
Jacked's example is the best since badman got to the top in the world just picking spec everytime he could
So if you pick an OP hero you can basically get any mmr if you're good enough
Only wyvern? LC definitely is a counter against meepo with his skills and correct item builds, including aghanim.
io. got to 1 0 0 0 0 M A T C H M A K I N G P O I N T S back in '99 just spamming that hero. dotabuff obviously didn't pick it up because obviously
In that aspect doesn't LC counter every carry?
People will say earthshaker and aoe like sven but good meepos play around that fine. I've only heard good meepos really bitch about wyvern.
Badman spectre is the best example of successful spamming. But that was before you could ban heroes in ranked. Once you become known as a spammer people will start banning your hero so you'll need to be able to play a second hero at that level to maintain your MMR.
Why is it so difficult for people to answer the initial question lol?
And Maverick brings up a good point--let's assume that they won't ban your only spammed hero, just for argument's sake : ) .
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Post dotabuff to provide support for your answer--theorycrafting not allowed. Anecdotal evidence is okay.
Another way to ask this question is: if those with 7-9k MMR were to only play their best hero, would their MMR drop, increase, stay constant?
Another related question is: if those with 7-8k MMR were to only play their best hero, and they always first-picked this hero, what would happen to their MMR?
People always say counter picks/picks are important. I'm not disagreeing; I'm just wondering to what degree.