Just my opinion, and I do agree that the audition itself trumps the resume…but as far as the resume itself…it is not so much WHAT is on the resume, as what you’ve learned along the way from all those experiences and training. So, if you have had training in acting, singing, and dancing, and have experienced being in various types of shows, all that can translate into being able to give a good audition. Training and experience (inc. experience at auditioning itself) helps you do well in an audition. So, it matters in that sense…what you went through to acquire that resume, rather than the list of facts themselves.
But I also agree that the resume is looked at (or they wouldn’t bother to ask for it) and while it is not more important than the audition, it gives them a sense of your background…how much training you have had, which types of training, styles of dance, kinds of theater experiences and roles you have played, who you may have worked with, and other helpful skills. And yes, these things may come up in the audition room. I recall my D saying that at one audition, the auditor mentioned knowing of her voice teacher and asked about that. In another, the person brought up that she had been in All States, etc. And yes, it showed things like being able to play piano and sight read. These things don’t get you in, but it just gives them a picture of who you are.
I wouldn’t do something so you can add it to the resume. I would suggest getting training in the various skills needed in musical theater and also garnering experiences doing theater. It is this training and this experience itself, that will help you be ready to audition and have some level of skill and development of talent to be considered. So, accrue things on the resume for the experiences themselves.