I still say that Joan was a feminist, and there are many ways to be a feminist. She didn't know it, but she was. Peggy, Bobbie, Rachel, and the most stereotypical, Faye are more easily defined as feminists. Megan thought she was, but her actions, completely dependent on a man's money after she married, kind of fuck that up for her.
Anyway, back to all the Harry comments which I will address at once.
I think Harry definitely had a defined roll on the show, and I think it was a very good one. @sistermagpie pointed out a lot of it in her post. I think I will just do a list from start to finish, I'm sure I will miss some.
Harry was the "average guy." He wasn't as good looking, he was married, had a kid, was in a job that could disappear at any moment, and wasn't making much money. He tried and failed to pal around with others, but aside from crude jokes (such as the stuff about Megan after her song/dance) he was just there, never earned much respect.
His shining moment was to realize that he better figure out a new job and fast. He did his research, realized that other companies had a dedicated Media Department, pitched it, had it approved, and starting with a one man operation built it up. Computers came in, he noticed, wanted more power, and pushed for that as well. Those things all helped the company, but his concern was helping HIMSELF to have a secure/respected position. (nothing wrong with that)
Hollywood and California happened. He'd already cheated on his wife once, regretted it, but now all kinds of women were suddenly available to him. Why? Media. He might get them a gig in a commercial! In addition, he now had all kinds of powerful connections with the Hollywood elite. He could have any babe he wanted, or most of them. It was the sixties, sex, drugs, rock and roll, parties. He started eating salads without dressing and getting a tan.
In the middle of all of this he does two very kind things. He saves Don's ass, in spite of Don hating his guts (which Harry didn't really know.) He thought it was unfair what they were doing to Don, and risked quite a bit to warn him. That resulted in Don saving himself, but without that head's up from Harry? Don was over. He also saved Paul. They had also been "friends" (Harry thought all the original guys were his friends.) He saw Paul drowning, and threw him a lifeline. So, Harry is not all bad, actually he has some very good qualities mixed in with the odious, sexist, oblivious qualities. In short, he is a "whole" human being, not perfect, not evil, a mix of qualities, like most of us.
While others are unhappy with the move to McCann's, Harry is content. He is getting yet another promotion, will have the huge department he always wanted, more power, and now, he knows all the players on both coasts and can really shine. He's also surrounded now with a bunch of neanderthal men. He's found his tribe. Still, he tries to maintain his (to him) previous work-friends. He's rebuffed a bit, but who cares? He's finally in a place where he fits in and is appreciated, with more money, more power, and more respect.
I don't think Harry was an add on at all, at least no more than others out of the core Peggy/Don, and sub core Roger/Joan/Pete group. The Harry character could actually easily be considered part of the sub-core group really.
He did quite a bit on this show, moving the times along, and to me, he was a very well written character.
EDITED TO ADD:
Through Harry's character's actions we moved from the fifties in NY, to the new decade of computers, and also to California. Don, of course, also helped with the California POV to contrast with the NYC lifestyles. So, for story, his character was very useful in both introducing interesting new things, social commentary, and how advertising evolved as well.