I am wondering if Office add-ins will disappear if I re-install office 2010 on my work computer. I work with finance so the add-ins are very important for my job. I have been searching the web a lot but can't find any answers.
This depends on what kind of Add-Ins you use.
STARUP Add-Ins
If you have "Macro" type add ins sitting in your STARTUP folder or even maybe in your Normal.dotm they will be gone. Because the STARTUP folder is usually set to the Office installation directory. It could also be changed by your company to a central folder. Then they would remain.
COM-Add-Ins
If you have COM-Add-Ins it depends on their installation location. Normally Add-Ins won't install into the Office installation directory (you'll need to check). After a re-installation of Office 2010 you probably have to repair them so they are registered properly again. It depends on the Add-In maybe you have to reinstall them as well.
Actions/XML-Schema
If you have actions installed I can't really tell you what happens to them. I've no experience. Maybe another answer or person can help here (feel free to edit or comment on it).
How to proceed?
As a start you need to investigate your installed Add-Ins follow this Microsoft link here. After you know what you have you can come back or decide what Add-Ins are critical for you to keep. Figure out their installation location and/or installers and backup them.