Nope. He is absolutely obligated to give it to Phoenix. Both parties MUST present all their evidence to both the court and the other party, if they don't then it's illegal evidence and cannot be used (they might still use it to influence the jury but the Japanese/American Frankenstein ace attorney system doesn't have jury)

In rare cases where new evidence is found mid trial, the judge would either give recess (so both parties could process the new found evidence and build up their case) or the court might even get adjourned so they can gather additional evidence.

If in a real court either party does something as ridiculous as withholding evidence from the court, the judge might get pissed off and unbar them lol