it will do it regardless(kinda), but it would have been good, if you made a backup of itunes and transferred to this new one, and if you didn't de-authorized that itunes on that pc, it is stuck there, no worries tho, you have 5 authorizations, you will use one on this new pc.
here is what you do, authorize this new pc first, connect to your ipad to itunes, right click on your ipad in left screen, you will see 4 options, and select transfers purchases first, and then backup after....this way your new pc is up to date with what is on your ipad.