Basically, if one player is online in the region and the rest are offline, it only has positives:
1) If you are buying service from the other cities that will continue, and you will spend money for those services.
2) If you are selling service(s) to other cities that will continue, and you will get money from it.
3) Interactions between cities continue in all normal regard; however, if you outgrow what you need from another city and the players are not online, you will have to provide it for yourself.