I don't know about the termites - and I don't know about outside ants.
But I can tell you that this year we have had a lot of very tiny ants
in our kitchen. And I learned one thing....Terro that was left over
from last year would not work on them. I tried it several times and it
did nothing. I went down and bought some new Terro .... and the ants
were gone almost overnight.

I doubt if the ants killed the termites. If this is an old shed (as
opposed to main house where you live) I would call around and find some
termite poison and try to treat it myself.