By definition your room is not an anechoic chamber so it will corrupt the phase and repeatedly so.
Direct sound that is phase and time aligned, reaches the ears as such.
The issue/question of how much reflected sound gets integrated with direct is too situation/room specific to make universal pronouncements about how much phase gets corrupted, or about what we can and can't hear with respect to time and phase alignment.
I know it doesn't take an anechoic chamber to help separate direct from reflected, to get a handle of the value of phase and time alignment. Constant directivity speakers with a defined narrow pattern help, especially in a larger room.
Outdoors really helps/works, and ime, can make you think twice about the "value and appeal" of reflected sound... (per widely accepted/quoted research).
btw, fun short vid about the sound of a balloon pop.... outdoors, different rooms, and an anechoic chamber at the end.
Outdoors clearly is a long way from sound sucking anechoic..
edit: grammar
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