Could a crypto system that uses non-FIPS crypto but then upgrades complete to FIPS be FIPS certified? I know most people around here (including myself) are anti-FIPS, but I have a FIPS related question.

Could a crypto system that is not FIPS, e.g. one based on primitives like Curve25519, achieve FIPS compliance if it is capable of upgrading to FIPS algorithms/implementations in a way that is complete. By complete I mean in the upgraded mode it is using only FIPS compliant crypto and the upgrade occurs in such a way that all the previous security guarantees are re-confirmed using FIPS crypto.

Or would the mere presence of non-FIPS crypto at any stage of the system invalidate it for FIPS certification?
Yes, a device that is FIPS certified need not be restricted to using only FIPS-approved algorithms.  For example, in your case, FIPS has no problems with you supporting Curve25519, as long as the user can turn it off.  That is, the device will need to be able to be set in a mode that it performs only FIPS approved algorithms (and the FIPS approval documentation will have to explain precisely how to do that).

You specifically asked about 'crypto system'; if you're asking about a protocol, a protocol is not FIPS approved; FIPS approved devices, not protocols.