The cans you recycling will be crushed and cut anyways, so crushing the can before recycling is fine, but keep in mind, your bags might weigh so don’t over fill.
If you’re trying to save space, then crushing the cans will be a great idea, but fill up large bags with crushed bans would increase the weight exponentially. Also crushing the cans would create syrupy mess on the floor which you crush it on.
Either way, please remember to Download RecycleBro to help you get rid of your cans and bottles, or to help you find free cans or bottles.