Not a crazy question at all! I can't promise what HWT could do for an adult but I can tell you how it helped me.
I was the daughter of an Elementary School Teacher with PERFECT teacher handwriting and I was a "hopeless" case. I always held my pencil wrong. I was put in Special Ed in Elementary school to "help my handwriting". They tortured me with every possible device to correct my grip (which was "fisted" in 1st grade). I still remember getting straight C's in 5th grade for "handwriting" which I felt was so unfair since it was not taught and no assignments given and I had no chance to improve. All else were A's in my gifted program.
I spent 2 days at a handwriting workshop to train HWT instructors to learn how to help my son and other children. Day one was PreK, Day two K-5. On day two, I called my mother nearly in tears... the way they taught... I GOT IT! I had written PERFECT cursive in a practice we did (it was combinations like "or" and "ar", "wo", etc). It had been impossible for me my whole life and in a few hours, I COULD DO IT!! I handwrote a cursive letter to my mom that night. She could not believe it. Now I practice a little here and there so it is becoming more natural and less thinking... but with their methods and materials even I can have that clear and pretty handwriting I wished for as a kid.
Grinity-- you hit the nail on the head! It is TOUGH to be a GIRL with LOUSY handwriting. My mom, a MAJOR perfectionist, would unfortunately remind me how my handwriting "made me look stupid." Which was an extra help... She jokingly asked who I got to write the letter for me since she could not believe I wrote it. I'm one of 8 kids and the one with the truly atrocious handwriting... or was the one.

I do need to get more involved in the Gifted World in my area. I expect to start having more of those opportunities now that my son is identified and old enough to begin participating in programs.
MumOfThree-- I hope that answers your question. It would be a pretty cheap option to try HWT. I know it has transformed me and my son. The books are inexpensive (like $7.50 US for a workbook) and you wouldn't need all the "extras" which make it fun for kids since you have your own motivation to do it. (Unless of course you have a child that could use it too b/c then you can get the extras and do it together! :)) It's written by an OT but loads more affordable than OT services.