Pretty sure it won't. Powering down removes all apps from RAM, forcing a clean start. The only difference is the list, and the list is nothing but a list. I'm not aware of any instance where a power down and removing the app from RAM made a difference. One is simply more convenient than the other if only one app is misbehaving.
I admit that I've only tested a few apps, but as near as I can tell an app that remembers it's last state does so wether your clear it from the multitask bar, restart the iPad, or do a reset. Those that start clean, also behave exactly the same in all three cases. I remember reading something in multitask behavior that said the developer was responsible for saving app state when an app closes; so that makes sense.
I've also done restarts, then monitored the RAM while clearing the list. Any difference in RAM was too small to see over the normal fluctuations in RAM use.
But if you've got information to the contrary, I'd love to see it. I'm open to being wrong.