What Happens When You Upgrade A Theme

All you data such as posts, users, etc. is in the database so ugrading should not touch that, BUT make a backup. If you have changed any code in the themes files those changes most likely will be lost so if you replaced header images, etc. have copies/BACKUP.

But probably the best place to ask is here, https://www.solostream.com/forum/

Thanks for the support. What about plugins? Will they remain untouched as well?

They should. The plugins folder is not in the themes folder.