George,
I think this is possible if you can work out a jig system which orients the workpiece (printed item to cut) with your laser. Think manufacturing jigs here but certainly low cost like a sheet of MDF (or other flat material) with round pins which will be used as registration points.
Think about creating computer file templates which have built in registration points on the drawings like round holes which could be aligned to a jig on the laser table. Then generate your drawing on that template so that every drawing will have the same "dots" in the same locations every time. If you are using the vacuum tables I referenced in a prior post you'll find they have sets of pin holes already layed out in very precise 4mm grids you can use.
Say you have a color laser page 8.5" X 11", portrait format with an upper right "dot" and a lower left dot that is your registration location for the printed paper. Then print your drawing and place on your pre-located jig on the laser table. Remember the laser will have a home position (x=0 / y=0)where you should be able to use trial and error to position the jig where the dots will be in the right place every time. Then the matter is to have the print driver work within your software where you simply "print" the cutout direct from the same software you generated the drawing in.
To do this with Corel and these Chinese lasers you'll need Corel 11 or 12 because they don't yet support CorelX3. Otherwise you must export a drawing into their software and cut from that. Not impossible but certainly another step.
If you can't picture this give me a call. I've sent you my telephone number in a PM.
Pete