Sure, you can deal damage to monsters without actually actively playing. Just buy levels in the "Auto-Fire Cannon" skill. This will keep you firing once per second without actually having to click anything.
At the very beginning, you won't be able to do much damage at all, and it may seem like you can't earn coins as a result. Don't worry - you'll earn coins passively even if you do no damage, just by having loaded the game at least once per day.
Check in periodically and you can spend your accumulated coins on further upgrades, like the Advanced Targeting skill (similar to, but more powerful than the Auto-Fire Cannon). Elemental ranks give you damage multipliers as well. Armor is also worthwhile, as it keeps you alive longer and thus doing damage more frequently.