Can a push button be connected to a twinkle board.
Almost certainly. If you provided a link, the answer could be definite.
I tried attaching the push button between the cell battery and twinkle board:+ in cell battery to S on push button, S on Cell battery to + on twinkle board. - on cell battery to - on push button. - on push button to - on twinkle board
A picture is worth a thousand words. I get lost trying to follow that.