No, by design the TOTP-specification RFC 6238 has been engineered such that it is very very hard to reverse engineer the secret key from one or a sequence of verification codes. The Invantive Authenticator has some functionality to determine whether a verification code can have been issued based upon a known TOTP secret key, but that is a brute force approach which will not establish the secret key.
On Exact Online you can reset the secret key easily. For more information on the process in Exact Online read Circumvent Exact Online 2FA to avoid entering PIN-code every ten minutes.
Changing the two-step verification secret key should no affect the validity of existing refresh tokens, nor should changing the password of the user do. It are separate sets of credentials.