If it's flat and smooth there is no reason it wouldn't work! With this said, 2" is rather narrow and I'd personally prefer it to be at least 2.5" or even 3" but you'd just have to adjust the x-strokes. The photo doesn't really show the leather clearly, which may mean the quality is not fantastic.

Trying to save money on a strop, I'd go with denim in all honesty. I have a selection of nice leather strops but lately I've just been using one that I made from a pair of jeans - it certainly works well enough.