Normally, I say no. You should dig anything that could be gold. And normally I dig all pennies, even on my CTX when its saying 12.37...which is most likely a penny because there is gold that will ring up the same as a penny. Having said that, there are times when I might choose to ignore them.
For example, this morning I was in the wetsand, which is mostly sanded in around me so its only recent drops. I found one spot where I was getting hit after hit. After digging up about 10 pennies I chose to ignore the rest of the 12.37 numbers at this spot. Its very hot out so I can only dig so many times before I need to leave so I wanted to maximize my time by digging only good signals. Did I miss anything good? More than likely not. I think someone dropped their change in this area. In that spot I also found several dimes and that was it.
So I do recommend always digging pennies but if you run into an area like I was in this morning then I think its ok to ignore them, especially if you have limited time and/or other spots to search.
The photo was taken when I took a 2 minute break to wipe the sweat off of my face because this heat we are getting is unbearable.