Why not? It would be equivalent to a murderer specifying two witnesses to the murder, and subsequently two other witnesses came to court - would you question their validity?
There is no way to disqualify somebody else's testimony.
As explained here, the source for the designation of witnesses is the Ritva Kiddushin 43, where this concept is brought as a way of getting around a potential problem of invalid witnesses becoming part of kat (set) of witnesses, thereby invalidating all of them.
The whole necessity for this is because for eidei kiyum (witnesses necessary to effect the Kiddushin), all present will automatically join into one group [because the 'testimony' is the watching], without specifically designating a different set. In your question, regarding eidei birur (for testifying in Beis Din), there is no reason why invalid witnesses would invalidate the Kosher witnesses unless they testified together in Beis Din. [See Rishonim Makkos 9]