No. A GMRS license permits one to transmit on GMRS frequencies only. An amateur radio license permits one to transmit on amateur radio frequencies only. No reciprocity exists.
If you wish to transmit on amateur radio frequencies, study for, and obtain a amateur radio tech license. With a bit of study, the test is fairly easy to pass and the cost of a HAM license is much cheaper than a GMRS license. Many here on this forum, including me, maintain both licenses.