Rastus, while not exactly interactive, you can set the Info Overlay to display cropped pixel dimensions, in View Options. Additionally, you can see the original and cropped pixel dimensions in the Metadata Panel in Library.
As far as up-rez interpolation of the image, yes, you're correct, this will 'degrade' the images. Actually, semantically, it's the cropping that degrades the images, the interpolation is a mathematical best guess calculation to repair the damage.
When working with Lr, it pays to think about crops in terms of X x Y ratios, but for down stream utilization, get used to thinking in actual pixel dimensions. Lr can either downsample and discard pixels for web displays, or interpolate and create pixels for large format printing. In either case, something has to give.