No problem. You're correct, if you were working with pixel sizes and were printing at 300 dpi, and wanted it to be 9 x 7 inches, the correct size is the number of inches x the dpi, so as you said 2700 x 2100 pixels would be correct.
Using physical dimensions when creating a new painting in ArtRage ( e.g. inches ) will give the same result in terms of pixels. So if you create a new painting, set the DPI to 300 and the dimensions to 9 x 7 inches, it will give you the correct number of pixels ( 2700 x 2100 )