Yes, you're doing the right thing. You can select a background image with a texture and color close to the paper you'll use at the print shop, and add your design with the "multiply" blend style over that background.
If you're not sure what paper to use, try to search for the most standard ones. At the limit you could even scan a sheet. There's usually not a lot of variation between each type of natural papers if your project is not a big budget one (eg. the print shop will most likely use the most standard and common paper).
I don't recommend you work in "multiply" mode though; you should do that "multiply" effect with a JPG or a flatten PSD that you import in a new file with your paper after you're almost done or a few times during your layout process.
Why I don't recommend you work like this is because you're not even sure of the paper and this could distort the results based on a wrong screen preview; it's better to work on your design the exact same way you would do your design for an uncoated/matte white paper in this case, and "test" it after you're done to see if anything should be intensified. And anyway, you can't compensate so much since you're always limited by the range of colors and density the CMYK or 1-color printing can do! If you use a red at 0-100-100-0, you can't make it more red, that's what I mean. But you can indeed boost your contrast a bit more, while keeping in mind that your design will probably be printed on a porous uncoated paper and this will make it look darker a bit.
Using the "multipply" blend mode isn't 100% precise but it usually shows a good preview of what you should expect to see once printed. For your separation, the only thing that it will show you is your color density but it might not give you a lot of clues about the result with the paper.
Since the ink will be "multiply" as well on the paper when printed, you don't need to be too worried about it. For example, even if you print a yellow on a natural paper, the 2 will add up the same way as your design blends with your textured background when you do a "multiply". Inks are semi-transparent and wet, they get absorb by the paper; you won't get any "pure color" on a stock that has already a tint. So all you can do is to make your colors as good as on a white paper. Of course there is a bit less contrast but the only details you could "lose" are the ones that are below 3-4% density... but that's the same for any other kind of stock.
So my advice is to work the same as for a normal white uncoated paper. And then verify your work the way you described; with a textured paper background and the design in "muliply" blend mode. And if you want to make sure it really looks good, nothing stop you from buying some natural paper and printing a proof with an inkjet.