I think it's highly unlikely. They need to find somebody whose stature would be increased by becoming the chairman of alphabet in about the same proportion as the prestige Alphabet would gain by having that person as their chair.
Obama as their chairman would be a huge win for Google, but I feel like he probably has better things to do. As a former president, being tied to Google would only hinder him in lobbying goverments for whatever he chooses to lobby for.
Objectively speaking, he would generally be considered likable by about 47.9 [1] of the voting public. It wouldn't be unreasonable to assume that the vast majority of employees of either Alphabet or Google would agree with your assessment, and indeed likely most in the tech sector. But I'm not sure any polarizing figure would be a good fit outside of those niches.
47.9% (on average) approval rating by Americans for his job as President (and consequently positions his cabinet, Congress and his party took). It's a barometer of how Americans feel about the USG, too.
If you polled him right now across worldwide audience about his stature, it would probably be north of 70%.
(Perhaps the departure was predicated on Obama agreeing in advance)