I'm going to go with "No."
I don't have an active data account for the iPad, so I tried this on my iPhone. I activated the iPhone's hotspot feature and connected the iPad to that hotspot. Then, I put the phone to sleep (pressed the button on the top. The connection is still active and I was still able to access the Internet (among other things - I also tried the App Store ... no problems).
So, given that it works fine when the iPhone is asleep, I see no reason why it wouldn't work the same if you were using the iPad to provide the hotspot.
Marilyn