I think it's an TEMPORARY item that alters the state of Mario, allowing him to preform actions he can't normally do.
Jäzzi– You unlock this door with the key of randomanation. Beyond it, is another chatroom. A chatroom of sound, a chatroom of sight, a chatroom of mind. You're moving into the chatroom of both craziness and cyberspace of stories and cussing of messages. You've crossed over to the Zeldapedian IRC. TALK– Editcount
In agreement with CoCat. From what I picked up, the P-Balloon is needed to complete the level. It just doesn't seem like a power up.
The same argument can be used for many power-ups. The P-Balloon also appeared as an optional item in Super Mario World, although it was required for one level. But it was a secret level. "So what", you may ask. "It still is required!" Well, the Boo Mushroom, Bee Mushroom, Spring Mushroom, Rock Mushroom, Fire Flower (in SMG), Ice Flower (in SMG), Cloud Flower, Metal Cap, Vanish Cap, Wing Cap, Yoshi and all of its SMG forms, and the Spin Drill are also required to complete at least one level. Also, what exactly do you mean by "temporary"? Do you mean a time limit or something?
Technically the level has a time limit before it disappears, that does not make a Power-up. I actually, just looked up what a P-balloon was (which I admittedly should have done earlier) and I thought it was something totally different. In Super Mario World 2, there's a giant balloon you ride on, and I thought that was what we were talking about. I take it back, that is a Power up. As it is temporary, alters Mario's state and allows him to preform an new action.