If you check in at T1 you can clear immigration there and freely move between T1 / T2 and T3. Many do to lounge hop. (There's an open air swimming pool, T3 I think, but stand to be corrected, a few bucks to use. The trains between the terminals are fast and generally reliable.

If you are asking if you can use a T1 boarding pass to clear immigration at T3, the answer is more nuanced. It will depend upon the protocols TK have in place with the airport, if you want to do that I'd check with the boarding pass ticketing agent. Although there are many anecdotes on these boards of folk entering non-departure terminals with the carrier they were on, it doesn't work with all airlines at all terminals with all manifestations of electronic / physical / home printed boarding cards.