If the shock is blown it definitely will. I've played with this topic with my last project vehicle. Going from gas charged to hydraulic drag shocks was worth a 1/4" drop up front. Push a gas shock in...it pushes back. Hydro shock...it stays put. I'm betting his seals are blown in that shock.
Before that, I didn't think it would affect ride height either. Also found one older internet article from Monroe that verified this.
If the car is at a standstill it's not the shock, it's the spring. The shock does not have the strength to resist the car's weight, it is only used to dampen the reflex of the spring.
I'm with others, it's the spring. Either bad or seated incorrectly.