Not to pour too much cold water, but … probably not.
Cutting fabric with a diode laser is do-able, but will be difficult on the scale you describe. The key problem is keeping the fabric flat with clamps / vacuum / pins on a platform that must also be flat over the entire surface. The overall tolerance is on the order of a millimeter, less than 0.1% of the platform size: this will be … difficult … with a flimsy base and lightweight rails.
Cutting “plastic” cloth differs from cutting cotton, because it tends to melt / char rather than burn cleanly. A visible-light diode laser has difficulty depositing enough energy into fabric, particularly for fabric colors ranging from white into blue / violet. Discovering how color interacts with material requires experimentation.