Not generally when it comes to CBP checking of passengers flagged by a name match done by/for CBP or supplied to CBP.

DHS TRIP-produced "redress number" is for purposes of not being confused with one of the huge number of people on one of the USG aviation-related passenger blacklists used by the TSA or CBP.

The redress number itself isn't generally useful when it comes to CBP checking of passengers flagged by a name match, but sometimes the process leading up to a redress number defintiely is useful. Since there is a substantial possibility that OP is being confused with someone on one or more blacklists, a redress number from DHS TRIP may be useful for fewer future problems when showing up at US port of entry. It's not a magic bullet to eliminate all such problems, but sometimes it has worked.