Is it appropriate to ask to see the results of this type of test (or any psychometric test) out of my own curiosity?
Before your face to face interview, it might be inappropriate. These questionnaire will likely tailor what sort of questions you are asked, and the interviewers likely don't want you to practice answering them.
After your face to face interview, it will likely be appropriate. The company might decline, as they're concerned that the info might be evidence in a lawsuit or that you might figure out what test they gave and help others game the system.
But for you personally it will hold no benefit after the interview except for self-education, so you wouldn't be seen as someone trying to fight against the process or trying to game the system.
At a company I worked for, HR was required to provide the employees with a copy of the questionnaire results once hired. You might frame it as asking if the company has a policy to give you the results. Also, I would not be surprised if certain jurisdictions mandated that you could have a copy of the results (akin to credit checks).