No. The TOSHIBA Tablet Easy Control is a tool that makes the use of your tablet / PC easier. However, this is not imperative to have so that your device will properly work. Also, not having this program will not interfere in any way in the computer's performance. In this matter, I strongly suggest that you continue with the upgrade without any worries.
To be noticed, that after the upgrading process is completed, you should visit the following website, search for your device model and download any compatible drivers for the new operating system.