I'm not so sure. For a start, even rich footballers have family lives.
I was living in London when I had my first child, and everyone we knew from ante-natal classes ended up moving nearer to their parents within 2-3 years. Being around family, and having that support, is really important if you've just had a baby. Being rich might mean he can travel more easily, pay for help, or move family, but it's not the same as being close to "home".
He may also look at Arsenal last year, where they really did have a great chance of winning the title, and think that being part of a team that wins their first title in twenty years would be a big achievement. Coming to City might be the nearest thing to a guarantee of medals, but there's still a huge pull to go and be there at the start of something.