Will "Auto Delete Old Conversions" delete my messages from all of my devices if using iCloud?
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.