Yes you can add the ITV channels, however access to them will be the same as on your old sky box, and I am not absolutely positive, yet 99% sure that you wont be able to record from them using sky+. This is because the ITV, or other channels you add, do not appear in the main 'All Channels' menu for recording purposes.
Check out this link for info on how to add ITV to your box.
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Having used sky+ for a couple of years now we wonder how we lived without it!