I can't exclude that possibility out of hand, but I'm not sure.
You could look at it in two ways: first, that if the pool of men available to be ordained were a lot larger (which it presumably would be if married mem could apply), then the Church wouldn't face the internal pressure to retain, shield, and try to salvage abusive priests simply because of a severe personnel shortage.
Second, you might imagine that if married men, fathers of children, were running the parishes, they would have less toleration for questionable clerics: they'd be more likely to take accusers seriously, and less likely to give their brother priest the benefit of the doubt.
Both of those suppositions are plausible.
On the other hand, abusers (even gay pedophiles) do marry and have kids, too. Recent revelations in the Protestant world have shown that married ministers can get into transgressive gay behavior on the side which goes on for years, decades. So if the pool of ordinandi were larger because of including married men, the number of potential abusers would be larger, too.
I also think that at the apex of the abuse (which would have been the 1970's), bishops were very much misled by the "therapeutic culture" to see acts of molestation as a matter of sickness rather than of crime or sin; it was thought that what Fr. Feely really needed was a semester at Therapyville and what the victim really needed was money for "counseling." The police, if they knew at all, were perfectly willing to go along with this approach. We all know better now.
Of course, the no-fault therapy approach conflicts with the age-old Catholic understanding of sin; but finding bishops who subscribe fully and wholeheartedly with he Catholic view of things has been an ongoing problem, too..
One thing about comparing hypothetical married Roman Catholic priests to married Protestant pedophiles, the screening process for becoming a priest is much more rigorous.
Allowing married men to serve as parish priests would help the Roman Church in a number of ways, the least of which would be a reduction in laypeople serving the Eucharist.