This question is a yes/no type. The answer (TLDR: "probably not a similar delay") is going to depend on the nature of the circuit and the valve. From an attitude control perspective, it is likely that you will need to model the centroid of the delivered thrust pulse as being later than the middle of the electrical pulse.
Lets imagine that the thruster is operated with a flow control valve that is monostable, i.e. an electrical pulse has to open the valve against a spring and at the end of the pulse the electrical command pulse is removed and the valve closes under the spring action. Lets say that the logical command is a top-hat function with near vertical sides.
- The rise and fall of the electrical pulse that is actually transmitted to the thruster valve could be quite different. Imagine that there is a logical command pulse within an onboard computer and a drive circuit that can deliver current to open the valve. The latter electrical pulse isn't going to be as clean a top hat function at all and may not have completely vertical sides. However this is within the control of the circuit designer and probably any deviation from the logical pulse will be minimal compared to what comes next.
- The flow control valve has to physically move, i.e. accelerate, the valve poppet/other feature so that it moves to fully open. There are different designs around some of which may have less inertia than others.
- The propellant flow will rise to maximum pretty quickly following the movement of the valve seat for a small thruster. Just as an aside, for a thruster involving combustion there will be another rise time associated with the combustion building up to maximum temperature, particularly for a catalytic thruster.
- At the end of the logical pulse the current collapses from the valve opening coil and the poppet accelerates back to the valve seat.
If we assume items 1 and 3 are too small to be of interest in a cold gas thruster then I suggest that item 2 is not going to be the same as item 4 because of the different physical processes involved.
I'd welcome contributions from those with some figures to contribute. If you look up web pages for common thruster valve manufacterers, e.g. Moog, Vacco then maybe they will have some valve performance figures.