Many parrots kept as single pets get very sexually frustrated, yes.
My eight year old female Meyers thinks I'm her mate and several times every year she wants me to mate with her.

She doesn't realize it doesn't work that way.

Wrong gender, completely wrong species.
But it's kind of sad really. I had a cockatiel many years ago who masturbated on a big "fake toucan" (those toys that can imitate sounds) quite often. Now he lives somewhere else with a cockatiel-girlfriend, so that was solved.
Even though Saga's been "married" to me for almost eight years, I will try to get her a male, and my three year old macaw, Cirino, a female. Because even if I don't let them have eggs, they do get a lot out of being mated to their own kind.
They are wild, undomesticated animals that we can't neuter, so their sexual needs are very much intact.
They
can live without if of course, but we all want to make the lives of our birds easier, but this is not a topic widely discussed...

That's probably also one of the major problems with forcing our parrots to live alone and "marry" us humans. Even if we could satisfy their social needs as well as another bird (which we almost never can), we could never help out with their sexual needs.
http://www.lafebercares.com/knowledge/learning_sex.html