can the drive train recall cause bigger issues?

can the parking rod recall eventually cause my front differential to blow if i dont get it fixed? cause the first thing i noticed was it would stay parked in park then it started slipping into neutral while driving then it started binding and wouldnt drive in drive sometimes and finally the front differential blew at the front left cv axle and i got a new transmission but would like the dealership to install it based on this recall but i cant tell if the two problems are connected
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