A:
If you have partitioned your external hard drive into 2 partitions, then lets say the drive letters are F: and G:. If you reformat a drive you have to choose either F or G to format. Your external drive is no longer a single drive virtually. Your computer does not see the physically single drive as a single drive anymore. Your computer sees it as two separate drives.
If you choose a drive letter, let's say drive F: and right click it when viewing it in the My Computer page. Right click and choose reformat, then it will erase every bit of data from drive F: but it will not effect the data stored on drive G:.
You are speaking of a program named Dashboard. That sounds like a third party software put out by HP or some other namebrand. That is not a Microsoft Windows software, but I could be wrong also, I am not an expert. But to answer your question. If your Dashboard program is creating a backup on drive letter F: (for example) and you format drive letter F then yes, of course, you will be erasing your backup files that were created by your Dashboard program. But this will not erase your Dashboard Program. The Dashboard Program is "assumably" running from your C: drive. Which is also where your operating system windows Vista is running from.
If you are creating an auto backup of windows on an external drive, then I have to compliment you. That is a wise decision!