Will I lose all my data if my iMac Logic Board is replaced?

BwiMac wrote:

I just haven't done a full reinstall and have read that the Mac will get a new serial number and thus causes problems when trying to reinstall a back up.

That's not true. The thing to do with a new Mac, or with a Mac that has a different serial number and looks like a "new" Mac, is to use Migration/Setup Assistant to migrate from the backup to the "new" Mac. Of course it will work with a different serial number, just as Migration/Setup Assistant works with a brand new Mac with ... a different serial number.

Not if you have made and kept a backup, before taking the iMac in for repair.

Hopefully you have a Time Machine or other backup in hand.

see > Other ways to back up and restore files - Apple Support

In that case, I would avoid a TM restore and manually copy files using Finder (re-install Apps afresh). It’s a bit more work, but zero risk. With TM, you also migrate hidden viruses, inconsistencies etc. some of which may have bricked your board, one never knows. I keep my TM leashed at all times (assuming he gets let out of the cage, which is once in a blue moon). You should too. All the best!

Possible. Did you back it up? If not, do so before giving them the green light. They won’t back it up for you, you’ll need to collect it and do it yourself.

You’re welcome.