No, priority filing does not give the applicant a longer period to demonstrate that they use the mark in commerce in the US. Filing with priority can help establish earlier rights to a trademark originally filed in a different country; however, it does not affect the timelines put in place by the USPTO.
If you file with a "use in commerce" (1a) application, you have to prove that you are commercially active in the US at the time of filing. A specimen (proof of use) has to be attached.
If you cannot demonstrate your commercial activity immediately, you can choose the "intent-to-use" (1b) filing. This way, you have approximately one year until you have to provide a specimen. Once the USPTO processes your application and issues the "Notice of Allowance", you have six months to file a "Statement of Use", proving that your goods/services are now available in the US market.