Using triac as a tripping device
Yes, but you need a resistor in series with the gate to limit the current. Read the data sheet to find the gate voltage at the desired trigger current. Make sure to give it enough current for all the applicable quadrants and for low temperature and worst-case sensitivity. Usually negative current is better, or necessary in cases where quadrant III operation (positive gate current, negative MT2 bias) is not guaranteed. 

That will turn the triac on. It will not shut off until current drops to below the holding current and the gate current is removed.