It seems to me that puzzle games (ie. Dr. Mario, Super Bust-A-Move) have more enjoyably complex gameplay than shooting games. This is due to the emerging patterns that the gamepieces make, whereas in shooting games it tends to be kill / be killed, and enemies disappear as fast as they come. What if we combined the two genres and had enemies that stuck together and formed new enemies / shapes under certain conditions?

Everyone likes different types of gameplay. Even when you combine multiple forms of gameplay into one game, you are not for certain attracting people from both genres. Some people who love shooters may or may not like the hybrid and some popel who love puzzles may or may not like the hyrbid. Make a small demo and see how it turns out.

Like a bunch of blobs that become a bigger blob?

Honestly I don't see how you can mix tetris with UT, can you elaborate a bit more?

Ikaruga was a great manifestation of this concept.

http://www.gamespot.com/gamecube/action/ikaruga/review.html