It's easy to notice carbon/water life because we are it, but most of our complexity exist within a rather narrow energy band (molecular electron orbitals with energy greater than a C-O and less than a C-H), so I think you're right to doubt that we'd recognize if there were a similarly narrow window into surprising complexity in the nuclear reactions that take place within the sun.

I expect there's quite a lot of "life" that we're overlooking, and that we're going to feel quite silly when we have whatever encounter causes us to broaden our definitions to include the rest of it.

Although to be pedantic, most definitions of life require that it be made of cells, and I doubt there are anything like cells in the sun.