I know you can hire some mercs during the game, but seeing that Skyrim is undergoing a state of civil war during the story, would anyone agree that Skyrim would be inundated by mercs from all over Tamriel during this period?

There are quite a lot but they've all been hired by other people. The ones we get are the unemployed mercenaries of which there are few.

Maybe maybe not. Some Mercenaries recognize the folly of working for a government or soon to be government and prefer to Freelance it for smaller organizations.

Most governments or revolutionaries have this blindside to using hired guns for a way, preferring to have those who are doing the dieing do so for a cause and not a paycheck. Irony is, they have to pay or support the followers just the same as they pay the mercs.

...but followers are a lot more likely to dig in when the fighting gets hairy than sellswords...

Well seeing as how a mercinary is basically just an oportunist thye would thrive in an environment where there is government turmoil. With military troops spread out thin and unable to watch over trade routes hireing a MERC would be the safest way for most to travel and they could help local police take care of anybody causing any local trouble. So yes a MERC would thive in Skyrim during a civil war.