Snack stick seasoned meat gets really sticky the longer that it sets and could be really tough on your stuffer to push that stuff through the smoker the next day. As others have said, the fresh sausage or even summer sausage would probably be OK. But, trying to push that sticky mix into snack stick casings would be a bear.
I really like to stuff all of my sticks and sausage right after grinding/mixing and then let hang overnight which allows the casings to dry out a bit prior to going in the smoker.
Obviously if you use the encapsulated citric acid, you need to stuff and smoke pretty quickly or the ECA will burst and mess up your batch.
Last weekend, we did grind up 250 lbs of meat on Friday night and let it set (covered) in our garage (nice and cool in ND), then mixed and stuffed the next day.