its not safe to do so as u r not an asylee yet cos just like u can't receive federal or state assistance with recomended asylum approval paper or Judge's approval with goverment's lawyer's promise to appeal the case, these two are not final although no one is gonna appeal your case as you were given this temporary approval from asylum officer and you are sure to get final approval unless you have past criminal record or your asylum application is later found to be false.
So you may not be given advance parole to travel, even if given,, you may have futur e problem. so don't do this stupid mistake!
take care