Yes sirA push-to-make pushbutton connecting reset to ground will reset the 555. The reset pin will need to be tied high with a resistor to hold reset high when the button is not pressed.
Is the diagram you provide a scope of the 555 output? If so, it seems that you want to reset the 555 just as the time period ends and the 555 performs a reset anyway.
When the time period ends the 555 will reset itself without any attention from you, as I said earlier..... reset the 555 just as the time period ends when i push a button ....