If I reset my time capsule in order to reset the password (which I don't remember establishing) will I lose my backed-up data?

As long as you don't erase the drive, resetting just returns the configuration to factory default.

Resetting an AirPort Base Station or Time Capsule FAQ

Resetting clears the network configuration settings only.

But, it might make sense to try to retrieve your forgotten device password first. See this User Tip from forum expert Tesserax:

AirPort - Regain Access from Forgotten Passwords

Data on the Time Capsule hard drive is not touched unless you perform a completely separate and deliberate Erase Disk operation.