Plenty of guys paint their Savage factory stocks.
It would stick, but to get the effect like on those two rifles of mine, you would need to do grey and black paint. First paint the stock grey (the lighter color) then do black diagonal stripes. After that go back with a sea sponge and blot grey over the black and black over the grey. It would probably be an effect similar to the picture of the top rifle which is 2 colors. If you like it then seal it up.

If you are talking doing the webbing effect like you see on some rifles, Then there are specialty paints available at the big box stores to do just that. They are typically webbing paints or marbleizing paints and come in many colors.
If it comes out shiny a top layer of Testors dull coat will kill the shine.
Just make sure you prep good first if you decide to do any painting.
There are lots of tutorials all over the internet for either style of painting.
Good luck and post pics when you're done.