I don't think it should be that subjective of a question. What your PTO is designed to do should be in your purpose.
If. like ours, your purpose is to enhance the educational environment and foster relationships among the school's interest groups, (paraphraed) then your idea was very good.
Even if not, it is great to get a goood rapport going with the teachers to let them know you are on the same side.
I'd be worried that your board has a little too much of an us vs. them attitude with the teachers. They need to lose that, even if there is some kind of history there.
Being as your idea would probably cost $50 at most but go a long way towards building a positive relationship with the teachers, I would not drop this if I were you.
(The idea is so good, actually, I hope you don't mind a hole lot if I steal it
)
In my view, PTO leadership should be doing two things -- allocating resources and fostering relationships. You sound like a great leader.
Do the bagels, too. If you are talking about your board's toes, I would not tread so lightly. You are the one in the hot seat. If there is trouble between your group and your teachers, it is you who will feel it most.