Wrong. Their traditions and rich history remain. The trophy cabinets would still show case their successes over the decades. They would continue to fill their stadiums. Even if their newer overseas fans from Asian markets shrank a little, they would still have huge fan bases domestically and abroad. They would still have large travelling supports. Their supporters would still always demand they competed and won trophies (remind you of any other set of supporters). Their names globally would continue to be recognised, respected and have longevity. Man Utd and Liverpool will always be compared with, and spoken about in the same breath as the likes of Real Madrid, Barcelona, Juve, Bayern.
If the Abu Dhabi owners walked away tomorrow, Man City would at best revert back to being an Everton or Aston Villa... and their fans would probably be more comfortable with that role - dreaming and hoping but ultimately being mediocre and accepting mid table finishes!