Can a level 18 player join a Giant mushroom battle?
Yes. A level 18 player can field up to 35 Pikmin, and a Giant mushroom only needs a squad of 20 to start — so you can join.
Your maximum squad size grows with your level, and each mushroom size has a minimum squad you must field to start a battle. If your cap is below that minimum, you can't join — no matter how strong your Pikmin are.