Only if they're long past this, don't care or use it to justify completely unrelated crimes.

It's possible but the villain needs to be really bad in order to overcome this Freudian Excuse. For example, Mothergod from Valiant Comics is listed as a Complete Monster on TV Tropes (she is not listed as PE on Villains wiki because she still doesn't have page). She was raped by her own father during her childhood but the narrative doesn't treat this as an excuse and she is very bad to the point where her actions can't be explained by this. Just read her entry on TV Tropes here:

• Mothergod, once known as Erica Pierce, is the instigator of Unity and one of the single greatest threats in the Valiant universe. Once a mentally-troubled young woman who gained the powers of Doctor Solar upon the destruction and recreation of the universe, Erica used her powers to live for centuries, killing her own alternate self and kidnapping her son Albert whilst sexually abusing him to gratify herself, twisting Albert into a monster. Mothergod takes over the Lost Land as a cruel tyrant while establishing mass slavery to build a gigantic city to base her operations in, having thousands of people and sapient dinosaurs torturously converted into cyborgs to wipe out anyone she deems a threat while keeping her "bionosaurs" sated with countless dozens of tribal slaves to feast on. In Unity, Mothergod reveals her intentions to obliterate the whole of space and time to recreate it all to her own design to rule over it as a god. Mothergod sinks the floating island of Japan and kills millions to spite Rai; has Aric's entire nation massacred while leaving him among a sea of corpses after a failed attempt to steal his armor; uses waves of her own armies as Cannon Fodder for months on end to stall the heroes' efforts; and finally tries to bring about the destruction of all of existence—with neither her own son or the Lost Land spared—in her final battle with Solar. Even with the excuse of a horrid abusive father in her past, Mothergod is afforded no sympathy and her ultimate fate is one pointed out as one she has condemned herself to, with even her motivation of bringing about an orderly reality simply a pretense to slake her psychopathic narcissism. At the end, Mothergod is simply a destroyer of millions whose endless atrocities negate any potential sympathy that could be netted by her.

Aside from the things that are mentioned in this entry, she also traps the main hero into a worm hole where he would experience his worst fears for all eternity and when he gets out of there, he is visibly exhausted and shaken from the experience.

There is one easy way is if the villain raped another child without remorse. That will go extremely against the villain's tragedy.

Of course they can. Roman Bridger and Piper Shaw are very good examples.

@KingBob123 I'm talking about those who were molested/raped themselves.