The general consensus on PUA from those who have done it for awhile is that it's good for getting laid if you get really good at it but it's not a great way to build relationships. This, of course, if a highly generalized and simplified version of the truth.
If approach anxiety is your biggest issue then it might be worth it just for the simple fact that it gets you approaching women and talking to them. A lot of guys in your situation once they clear that hurdle don't even need any of the other aspects of PUA. The most surefire way to fail is to never try and at least PUA encourages you to try.
Don't expect any magic bullets or quick fixes tho - fake promises of these things are one of the major issues that I have with the PUA community. It's still all on you to overcome your fears of approaching and talking to women.
Personally, I would take the money you're thinking about spending on the PUA workshop and instead spend it on some extracurricular activity where there will be a lot of women around for you to get accustomed to their presence and talking to them. A dance class is one great idea imo - gets you up close and personal with women so you have no choice but to get comfortable with them and when you get good there's a good chance your social life takes off which will only make it easier to meet women in the future. I used to take salsa classes and it was absolutely sprawling with women, some of which were young and hot.
They see indoctrination and they call it "morality", "professionalism", or "maturity" depending on the context.