Regardless that the flinger is supposed to be crucial in attacking, being the building that flings monsters in, you can still attack even if it's destroyed. It's only use is being part of an NEC (Never Ending Chain) to stall monsters.
Some time ago, when attacking, if you decide that you don't want to actually attack any longer you will lose all monsters that you have added to you flinger.
Example: You want to attack a wild monster tribe. You click attack and are ready to start flinging in you monster so you add 20 tanks. Then you notice you don't have the amount of tanks that you thought. If you click end attack any monsters that you have selected and not flung in will be lost. To avoid this remove all the monsters from your flinger then click end.
(If you look in the update log, you will see this bug has been fixed.)
It may also required to upgrade it to level 4 so you can attack more farther.