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Yes, the threshold for hearing audible phase shift on an analog equalizer can change significantly depending on the audio system and listening environment

How the audio system affects audibility

Room acoustics

• Acoustic masking: In a typical listening room, sound reflections from walls, ceilings, and other surfaces create a complex web of constructive and destructive interference (a "phase soup"). This ambient phase distortion is far greater than what an analog EQ introduces, effectively masking the more subtle EQ-induced shifts.
• Threshold shift: Because our ears are evolutionarily adapted to filter out the natural phase shifts caused by environmental reflections, the audible threshold for an EQ's phase shift is much higher in a normal room compared to a controlled, anechoic (echo-free) environment. 

Loudspeakers

• Crossover effects: The crossovers in multi-driver speakers are a major source of phase shifts, as different frequencies are routed to different drivers (woofers, tweeters). The phase shifts caused by a speaker's own crossovers can easily dominate and obscure any shifts introduced by an external EQ. This is less of an issue with headphones or single-driver speakers.
• Driver alignment: In multi-driver speakers, if the drivers are not perfectly time-aligned, it can create additional, audible phase distortion. Some high-end speakers, for instance, are designed to have all frequencies leave at the same time to ensure better phase coherence. 

Playback volume

• Audibility increases with volume: Studies show that phase effects, particularly in the lower frequencies, become more noticeable at higher sound pressure levels (SPLs). If you are listening at low volumes, phase shifts are less likely to be audible, but they may become detectable when listening at higher, more intense levels. 

Headphones vs. speakers

• Headphones offer higher sensitivity: Controlled studies have shown that phase distortion is more detectable on headphones than on loudspeakers in a normal room. Without the masking effect of a reflective room, the subtle changes introduced by an EQ's phase shift become more apparent. 

Complexity of the audio material

• Musical content vs. test signals: Phase shift is generally inaudible on complex musical and speech signals. It is most easily detected with specific, simple test signals, such as square waves or tone bursts, and only under very controlled conditions. A phase shift that is obvious with a simple test tone may be completely lost in a dense mix. 

EQ-related factors that remain constant

While the audible threshold changes, the physical phase shift caused by a given analog EQ remains constant regardless of the audio system. The EQ's circuit design dictates the filter's minimum phase characteristics, which means the amplitude and phase response are inherently linked. What changes is the listener's ability to perceive that shift based on the overall context of the playback chain.