Been searching for a answer to this for awhile. I assume you would not lose it but I would hate to find out the hard way. BTW playing on the Xbox.
No, you won’t lose your single player/co-op save. When you do start multi-player your characters will be per server. Meaning if you switch servers you’ll have a different one for each.
You should be backing up your single player save game anyway if you are using any major mods.
All it takes is to get one single update, have a few key mods broken, and end up with a corrupted/borked save game.
Take your save folder and copy it somewhere, it even allows you to then start over and revert back to your old save if you just copy it back 
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