I think you don't quite understand how retina works. Have you seen an iPhone's screen, especially when they switched from non-retina to retina? There was no visible loss in quality. The same applies here.
The retina screen on the MBP is pixel doubled in both directions, meaning that instead of 1440x900 like the old days, it is 2880x1800.
What that means is that each individual pixel is 4 times smaller than the old display. It also means that in scaled resolution, 4 pixels are playing the role that a single pixel used to.
This in turn makes everything seem sharper, more defined. In short, you will not see a loss of quality for youtube videos, they should even look better with all other settings left the same.
Go in a store and play around on one, it's free and you'll see for yourself.
I hope you're not buying a 15" strictly for watching youtube though, that'd be grossly overpaying for something an iPad can do