Sort of, but it depends on what you mean by "quantize it's beats". If you're thinking of this like a hardware groove box where you tap pads for notes and those notes can be quantized to fit within a tempo with swing, then no, Mobius does not quantize notes as you play them.
When you record a loop it will determine a tempo for that which can be used to generate MIDI clocks to send to a drum machine.
It also subdivides the loop into "subcycles" which can be used to quantize other functions like Overdub, Replace, Mute, etc. and these subcycles could represent "beats" but they don't have to. You pick the number of subcycles in a loop with a parameter, it doesn't depend on the tempo of the recorded loop.