The credit freeze should already prevent unauthorized use of your credit reports. While it shouldn't hurt things to have a fraud alert as well, it probably won't add anything either.
Also, it shouldn't be necessary to remove the fraud alert before applying for new cards. It's just an indication that lenders should contact you before approval (though I'm not sure how many actually do this). To answer your question, though, it may take a day or two for any removal of freezes or fraud alerts to actually take effect.