Use 555 timer to output same interval as user presses a button
Yes, you can set a '555 to oscillate, and use logic to (1) count UP
at the oscillation frequency while the button is held down, (2) count DOWN
and set the output pin high, when the button  is released, and (3) reset the output pin low when the count-down reaches zero.

One or more 74HC191 counters would be suitable for the count function.

The '555 is intended to make a fixed time interval, so accumulating 
a pulse count (clocking) is the easy way to implement a variable time delay.