I am a knifemaker in New Zealand so I have some experience with blades. I can tell you that with a normal knife stropping is commonly used to prolong the edge of the knife as Rob Z stated before me.
It is also used to get the burr off a freshly sharpened blade. This is achieved by stroking the blade at a low angle with the spine leading along a soft material. The palm of your hand is a common one and is suprisingly effective. Canvas, denim and leather are a few others. This does not sharpen the blade but re-aligns the edge.
I doubt you could achieve much on the multi bladed shaving razors as you need to have access to both edges but the theory is there.
What the guy in the instructable is talking about is based on what I have mentioned above but will not work, jeans will never sharpen razor blades no matter how many times you stroke them. His tips about keeping them dry and clean is very true though.
Stopping blades from rusting is my biggest concern. Even if they say they are stainless they will still rust enough to destroy the edge very quickly.
Stropping your kitchen knives (a knife steel is a form of strop) and straight razors is a very good idea, trying to strop your shaving razor is waste of time.
Keep them clean and dry and you will get more life out of them.