Unless you were buying crack on a credit card, no. While credit scores can be used by companies to vet your fitness for loans, work, etc., they are not typically used in parenting evaluations.
This is a common scare tactic--threatening to divulge something unrelated to parenting to paint the opposite side as a bad parent. Frankly, unless someone is a real basket case, this will not make one whit of difference.
You would have to ask a financial professional about debt consolidation and credit score,