No, you cannot draw anything with Mach3, it will only read G code processed by a Cam Program like Mastercam or any other Cam Software.
They're some Wizards inside mach3 that will put out some G code if you buy the licence, I think, never used them.
Or if you are good at programming, you can write it in any word processor and load it with Mach3.
Or you can put simple line of program in the MDI page of Mach3.
They're are some nice little free CNC program editor on the net, just do a google search.
They're also some free Cam software on the net, CamBam is one of them.
Jeff