If you block a phone number in iMessage on the iPad, does it also block it on the iPhone?

Depends on whether you are using the same iCloud account on the device, or if you are syncing Contacts via iTunes, if you are syncing both devices to the same computer.

When you block someone, no matter which application you "launch" the block from (Messages, Phone, FaceTime) you are blocking the Contact. So, any app that uses that contact will see it as a blocked contact and will block any incoming activity to that app from that contact.

Here is a Support Article with more info:

http://support.apple.com/en-us/HT201229

Cheers,

GB