Mobile data failed problem

I had this issue initially as the iphone 7 was constantly searching for signal following an update it insisted on doing. Under settings in mobile data it says error so I can't do anything from there. Then I looked at about this phone - both network and network available are greyed out, can't do anything there. I have been through everything that has been recommended, tried it all and then wondered about erasing all content and settings, I got the following message - IPhone requires service - you will not be able to set up this iphone after erasing. a mobile data update is required before it can be activated again - obviously I aborted that plan. QUESTION - I am not sure if I dare to but, it is plugged into the mac, all updates (except the most important one!!) are done but it does give me the option to restore to a back up... Do I do it? Or will it close down the phone? Any help is appreciated