The best glue for teak is resorcinol such as two part "Weld wood". This is not used much today. Next best is a good epoxy--and G Flex is said to be the best of those. I did destructive testing when I was building boats and Rescorcinol was better than epoxy.
Titebond, Gorilla glue, as well as white glues have been used with reasonable results.
I use epoxy-and clean with lacquer thinner or acetone as noted above. The natural teak oils tend to make teak bonds more difficult. I do like to seal the edges of any plywood which might get wet--but below it is not as much of an issue. I prefer to use SS brads because of potential rust in salt water boat, and a nail set to push them below the surface. However, if possible I just use clamps, without brads.
You what propose will work, but I would use a glue which is know to work well with the teak.