Yes, it is possible. Below is a project I did using magnet sheet. But you do have to make sure there is NO PVC attached to your magnet sheet. (Even one use of PVC in your machine can cause damage.)
Since your sheet is already printed, here’s how I would approach the project. You’re going to have to make a custom jig; I’d make it out of chipboard or something that corresponds closely to the thickness of the magnet sheet.
Create a cutting file starting with a rectangle the exact size of your magnet sheet, and place your cutting outlines within the rectangle to correspond with all the printed pieces you want to cut. Use a different color for the internal outlines.
In the Glowforge, using a piece of chipboard larger than your rectangle (taped down to the crumb tray), set the rectangle outline to Cut and all the internal outlines to Ignore. Cut the outline and remove it.
Place your magnet sheet into the cut space, and after setting focus somewhere on that sheet, set the rectangle outline to Ignore and the internal outlines to Cut.
Be aware that cutting magnet sheet can be somewhat messy—it leaves little crumbs all over.