It might. More and more judges and evaluators are becoming familiar with parental alienation
and are willing to consider it as a serious issue; some custody evaluations are decided on this factor alone. Although evaluators typically refer to it as the "willingness to support the child's relationship with the other parent", it works out to be more or less the same thing.
If you can show credible evidence of alienation, it should be considered as an important factor in deciding custody.