iPad's Mail won't check for new messages in folders
Short of getting a different mail client on your iPad I can get you more than half of the way there.

Set up gmail as Microsoft Exchange server (leave the domain blank, add user and password and let it try to connect. When it fails, use m.google.com for the server and you can choose mail, calendar, address data to use ActiveSync)

Once the first mail sync starts, you can then choose days to sync and which subfolders will have push enabled. The mail badge count still only reflects unread messages in the Inbox, but you will get the mail notification sound/vibration for any new push message arriving in your selected subfolders. Your iOS device will be ready to go when you tap into the folders that have new push messages.