If I have my settings on continuous update back up, if I unplug My Passport will it “catch up” when I plug it in again?
Hello and welcome to the WD community.
If by catch up, you mean that it will update the files and add new files, then you are correct it does update the backup.
Thank you! Yes, that is what I meant by catch up 
Just also be aware that you may have to stop the continuous backup process before you try to remove the drive.
The backup process will tend to keep files open on the drive, and in doing so that can prevent the drive being safely ejected.
Would you recommend not doing continuouis backup?
That’s entirely up to you and your individual specific usage requirements.
I have continuous backup on mine, but I’m backing up to a networked NAS box (a MyCloud Mirror) rather than a plug-in drive so it’s a different usage case. If I were using a plug-in drive I’d probably do it periodically instead simply for convenience, but of course you then risk losing newer stuff between any failure and the last time you backed up.
And of course in that scenario you have to actually remember to do the backups, and have the drive in place to receive them.
