Yes.Most people are visually motivated. Do you move around much on stage? If you stand still, non-musicians in the audience will tend to assume that the cool sounds they hear aren't coming from you. Even the camera operators for big concerts are fooled, so they show the guitarist's hands when the bass is soloing or whatever.
So, for a win-win, dance around, move your hands more than you need to, smile, make bass-face, act like a star. Then magically you will be a star, and the other win is that the audience will have more fun.
I played in band in college... Mostly I played upright (though I feel better on electric) and it was kinda cool for the novelty of it. That was about it, though, recognition-wise.
Then we played a few gigs far away and I wasn't able to bring my upright, so I rocked out on electric. And boy did I ever rock out! I was jumping around playing everything with such joy and freedom! It was awesome.
Anyway, after the gig the leader was mad at me and I couldn't figure out why. Turns out she was sore because everyone kept coming up to her and saying things like, "hey, you guys were good. Who's your bass player? He was AWESOME!" ...and things of that nature. A bunch of people came up to me and said the music was ok, but I stole the show and they loved it. It did feel good to be recognized, but it felt even better to be free with the music while playing.
No matter how much I wanted to play electric after that, the band leader wouldn't let me. I played upright again for the next few months after that and then left the band.
So yes. Dance around! Have fun and get into the song. Better yet, let the songs get into you! You can't hide your enthusiasm if you let the music move you, and that enthusiasm is contagious.