A588 is equivalent to A709 Gr 50W. The A709 Gr 50 is equivalent to A572 Gr 50.
The answer is yes you can, unless you are working with a contract requiring otherwise.
I normally run D1.5 PQRs with A588/A709-50W so that the test will qualify the lesser grades as well.
I would carefully review the A588 MTR to be sure that the material fully meets ALL requirements of A709, because sometimes the documentation has errors and omissions.
I also would be checking my minimum chemical percentages and/or Carbon equivalency against the D1.5 requirements- some heats don't quite make it. Check the backing material requirements also.
I have run into some customers that want the base metal CVN tested, not just the CVN test required by Fig 5.1. For that reason, I also make sure the plate has been mill tested and reported on the MTR or I request the lab to test samples when the Fig 5.1 tests are run.
Chet Guilford
Chet Guilford