Will "Auto Delete Old Conversions" delete my messages from all of my devices if using iCloud? My wife's iPad is constantly out of space. Most of the space is used up by Messages, where her iPhone Messages sync with iCloud, and her iPad sync with iCloud, and thus, she copies all those large attachments to to iPad and fills up her space.

I found this article that talks about enabling the "Auto Delete Old Conversion" feature. However, before I do this, will enabling this feature on her iPad also delete messages on her iPhone and Mac as well since she is using iCloud Messages? She wants to keep all her messages on her iPhone/Mac since she has ample storage there.
You can consider disabling Messages altogether by going to Settings app → Messages → iMessage. This will completely disable Messages on the iPad (you won't be able to send/receive Messages).

Disabling Messages on one device doesn't affect in any way on other devices linked to the same Apple ID.

However, simply turning off Messages may not automatically purge the message cache.