Alexis,
Yes, the standard procedure for recovering a password does not cause you to lose your startup configuration information. The exact procedure differs slightly for different products, so I will use a 2900 series router as an example below.
A high level overview of the process is:
-Attach the terminal cable to the console port
-Reboot the router and issue a BREAK during the boot
-Change the configuration register so that the device boots to ROMMON (usually 0x2142)
-Issue the Reset command at the rommon> prompt
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Important Step for your Question:
-Copy startup configuration to running configuration (make sure you do NOT reverse this!!). This step loads your saved configuration into active memory, but since you are already in the privileged mode, you have essentially bypassed any security associated with the startup config.
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-Set the passwords that were lost
-Change your config-register back to the default (probably 0x2102)
-Issue a Write Memory to save your password and config register changes
-Reboot the device
Here is a more detailed Cisco Article:
http://www.cisco.com/c/en/us/support/docs/routers/2800-series-integrated-services-routers/112033-c2900-password-recovery-00.html