Short answer: Yes, though you'll have to define "much".
Long answer: First reflections and bass modes/SBIR will change the sound at "any" level, though at some point I suppose the reflected energy is low enough you can no longer hear it. You'd have to characterize your room to see if that is the case. But, room modes can cause peaks of 6 dB, so they will "always" be audible. Nulls can be very deep (I've measured 20~30 dB in typical rooms) so again will almost certainly be audible at 60 dB SPL. Reflections vary wildly but again it's hard for me to believe they would not change the sound when listening at 60 dB. Especially if you are mixing using near-field monitors. A lot of engineers position their monitors and damp the control surfaces to reduce reflections.