Are there any limitations to how large an artboard can be?

Yes, there is a maximum of 10,800×10,800 pixels per artboard (36×36 at 300ppi). If you have multiple artboards per page, the max size is 10,800 for the CANVAS, not per artboard. So for example, if the canvas is 4 artboards wide, the max for each artboard is 2700px.