I don't know if the research has been done but I know what I can see around me, and what I read in the papers and what other women that I know have gone through when giving evidence at their trial, and it is widely reported that fewer and fewer complaints even lead to court, much less to a conviction.
You're right that rape convictions are generally more difficult to secure than conscious for other types of offending. But I don't think this has a great deal to do with pornography consumption having normalised sexual aggression (indeed, no evidence supports this).
What I believe is hugely relevant here is the tricky great area of consent; since the only difference between consensual sex and rape is the victim having given or not given their consent, at any point either before or during the act. This becomes even more tricky in cases where women are raped by their own partners. Since these couples may be also engaged in regular consensual sex, physical evidence of rape (ie the presence of the man's semen inside the woman) becomes less reliable in court. Yet there may well have been an occasion in which the woman had firmly said "no, stop", part way through, which her partner chose to ignore. If he's ignored her pleas to stop, he has most definitely in legal terms committed a rape against her. But the issues and difficulties with securing a conviction in these cases, if the woman wished to, is that it is so incredibly difficult to prove or disprove consent (or otherwise) during the legal process. You often just have one person's word that they said "no" and the other person's word that they didn't hear this, or that it wasn't said. There are unlikely to be any independent witnesses to corroborate either person's version (for obvious reasons because it's an offence that usually takes place behind closed doors). This throws up massive complexities for the criminal justice system. They have to prove that the victim definitely did not consent - which is a challenge. It's in contrast to a physical assault, for example, where there will often be bruising and injuries that serve as evidence, which can be taken into account to help secure convictions. Additionally, there is no "consensual" version of hitting someone. Hitting someone is assault (at least in the eyes of the law), end of discussion. But having sex with someone can be both a consensual and legal act, and an illegal act, depending on whether consent was given or not. That's where the huge challenges lies for securing rape convictions.
And it is a huge problem, without a doubt. I don't know what the answer is. But I'm almost certain that widespread pornography consumption has little to do with reduced rape conviction rates; and far more to do with the complexities and difficulties of proving or disproving consent.