In theory, if you are close enough to the sockets, you might feel a tingle. Depends on whether the ground wires are any good. Most modern USA house wiring has the ability to detect what are called "ground faults" (i.e. the ground wire suddenly isn't working right). The circuit breakers would detect a huge surge when the socket shorts out, so they would kick out quickly. So any "zap" would be brief. But I couldn't rule it out that you would feel it.
As to "play the organ" - yes. I have played one musical instrument or another since I was six. Started with the accordian, also learned trumpet. But my best instrument is the organ. In the 1960s, home electronic organs were popular. (We were still 30 years ahead of multi-media computers.) Mom visited a local music outlet with a friend of hers from the school parent/teachers group. She won the door prize of an organ in the home and four free lessons. OK, obvious promotional stunt, right? It worked, though. She took the lessons but it happened in August when I was off from school. I had a chance to play with it. In a matter of a month, I was playing well enough that she couldn't let it go, but she DID upgrade it. Fast-forward to high school and I got a portable, VERY primitive keyboard. Started playing music with a garage band. Jump forward a little to college and we were playing on Bourbon Street in New Orleans. This was after hurricane Betsy did a number on a lot of homes and the club's owner had salvaged an old Hammond B-3 and an extra speaker (the infamous "Leslie" cabinet). I played that for a few years. Paid my way through college, no loans required. (Well, one loan from Mom for a grand total of $40 to cover lab fees.)
My senior year, I was doing some things for the music company that originally provided the first organ. One of the representatives of the Lowrey Organ company (a division of Chicago Music Co.) talked to me about being a roving demonstrator. Essentially, go out, do concerts, assist local Lowrey dealers by showing customers what you could make an organ do if you knew what you were doing. I had a choice of being a road musician or continuing to graduate school. I was thinking about it when two events helped me choose.
First, I played in the stage band for a concert with Sonny and Cher. Their lead-in act was Charlie Rich, the "Silver Fox." He had just had a pop-chart cross-over hit called "Mohair Sam" and was making the rounds. At the cast after-party, I had the chance to talk to him and let me say this first: He was a real gentleman! But he told me what life was like as a road musician. For more than 2/3 of your year, your license plate is your address and if you stay in the same bed more than two days in a row, you either had a vehicle breakdown or you ran out of gigs to play. That was what happened unless you were "discovered" and/or had a hit record. He said it took him 12 years for his first marginal hit.
Second, I met a gentleman named Eddie Baxter, who also worked as a road demonstrator for Lowrey. He had also done TV soap opera backgrounds when they were live with an organist as the only musician. And he had done stadium baseball games at Candlestick Park in San Francisco. So far as I know, he had never met Charlie Rich, but the stories they told me were damned near identical.
I chose the "graduate school" path and have almost never looked back. Now, I play strictly for fun. You can find pictures and recordings of the instrument I have, a Technics F5, on the Internet. YouTube may still have some music recorded by someone else, and there might be a few historical articles because the F5 was considered one of the top-of-the-line instruments for home use at the time. The organ I had during Katrina was actually an F3, but I found its "big brother" on-line several years later. Interestingly enough, I found it listed from a couple who were retiring and down-sizing. They needed the room more than they needed the instrument, and the husband had a stroke so couldn't play any more. I got it and had it shipped here. Four weeks later, a massive hurricane went through the Outer Banks. The F5 would have been under water if I had not given it a new home. Darn thing is a real beast, though, and is fully MIDI compatible if I had the right kind of cable. (I do have MIDI software elsewhere.)