Without Joshua Parlby, there wouldn't have been a Manchester City. There'd just be a record of a long-forgotten club called Ardwick going bust and resigning from the league in 1894 with Rotherham Town, who weren't re-elected that year, probably having had a reprieve.
I suspect that, 50 years from now, when Gary James's successor writes the history of this period with the benefit of hindsight, the Manchester City of the day will be a formidable presence in whatever format of the game then exists. He or she will probably ascribe the crucial factor in that pre-eminence to the ADUG takeover, so Sheikh Mansour will be viewed as the individual who most epitomises that.
I don't think you can split Joe Mercer and Malcolm Allison, because I don't believe either would have achieved anything like the same level of success alone. It's impossible to understate the importance of what they achieved. When they took over, average gates were at a quarter of the present level and we could barely scrape 8,000 for some games. The club was in such a state that two directors approached Manchester United with a view to a groundshare leading to a merger. I don't think it's fanciful to suggest that a poor managerial appointment in 1965 could have finished us as a force in the English game for good, leaving us just withering and dying in the second tier (or worse) as our support base gradually eroded and the United juggernaut drew in more and more local fans. Instead, Mercer and Allison turned us into a genuine big-time club again.
David Bernstein steadied the ship when we went down to the third tier and helped to create the conditions in which we could return to the top flight with a new stadium. That basically laid the ground for what's happened in the last decade. Others were obviously instrumental in that, too, but without the club being sorted out off the field, the revival couldn't have happened and Bernstein was the strategist who was behind it.
Obviously there are so many people deserving of immense credit for having given us magnificent service, some over many years. However, the above are the individuals I'd single out as those whose contributions strike me as the most transformative in terms of the club's development. To answer the OP's question, however, if you have to narrow it down to one, it would have to be Parlby because, without him, the whole venture would have been stillborn.
As for the biggest icon, a different debate, I really don't think you can look past Bert Trautmann because he's the one figure who embodies everything I want us to be as a club. He was widely recognised as a genuinely world-class player (including by his contemporary Lev Yashin, a man often hailed as the greatest of all time in Bert's position). His courage created one of the most remarkable episodes in English football history. He developed a wonderful affinity with the supporters despite a background making that a negligible prospect. He came from overseas and grew to love Manchester and Mancunians. He did so much to bring nations and peoples together. Those factors make him the figure above all others I look at as a symbol of MCFC.