It depends on the type of acetylcholine agonist that you're using.
Ex. Pilocarpine is a muscarinic agonist used to increase salivation for dry mouth in Sjogren's syndorme and radiation therapy. It does not have an effect on nicotinic receptors (muscles).
Ex. Succinylcholine is a nicotinic agonist used to induce paralysis for operations. It has such a strong avidity for the nicotinic receptors that it can bind and induce desensitization of the nerve terminal (phase 2 block) causing the cells to retract nicotinic receptors, so that additional acetylcholine can no longer bind to the cells, resulting in inability of the muscle cells to depolarize (potentially causing apnea and death). Succinylcholine does not have an effect on muscarinic receptors though.
So as you can see, it depends on the agent you're using.