The interplay of the glass transition with liquid-liquid phase separation (LLPS) is a subject of intense debate. We use the scattering invariant Q to probe how approaching the glass transition affects the shape of LLPS boundaries in the temperature/volume fraction plane. Two protein systems featuring kinetic arrest with a lower and an upper critical solution temperature phase behavior, respectively, are studied varying the quench depth. Using Q we noninvasively identify system-dependent differences for the effect of glass formation on the LLPS boundary. The glassy dense phase appears to enter the coexistence region for the albumin-YCl3 system, whereas it follows the equilibrium binodal for the γ-globulin-PEG system.