Usually when you freeze a CRA and apply for a credit card, they will either ask for a one time pin to pull the report from that bureau, or if you are proactive you can call recon and ask them to pull from another CRA.
Some report that Chase and other companies are a bit more lenient on requests to pull from another CRA, while it seems AMEX is firm on pulling only Experian.
You don't have to unfreeze your CR to apply for CCs, but it would be more work as every time someone wants to pull from Experian, you will have to call Experian for a one time pin to grant that request.