In theory the answer is yes. Since your design appears in the Zazzle marketplace, it is possible that someone could somehow stumble upon your product and purchase it.
Just being a designer at Zazzle means that from time to time Zazzle will most likely market your product/s. So there is a good chance that Zazzle may market your designs for you... but it probably won't happen a lot, if your designs aren't selling.
Affiliate marketers could also somehow happen to stumble on your store/products and choose to promote them, especially if the designs are amazing!
But the part that you did not mention in your post are the words you use to title, describe and tag your products with. No matter how amazing your designs are, it is very unlikely that they will be found without descent words behind them, even in the Zazzle marketplace. After all you are competing with 900+ thousand designers and millions of designs/products...
Zazzle is kind enough to provide the platform, the design tool, and the marketplace to all of us for free. In doing so they do not promise to advertise, promote, market or otherwise assist us in making sales. While just designing and not promoting on your own will probably net you a few sales a year, chances are, that that return on your effort will mean that you give up. After all most of us design in order to earn from our efforts. There are some that just enjoy putting art on things, without the expectation of making sales... you may be in that boat... but most of us want to earn money from our efforts.
The only way to do that is to get eyes on our products. This is done via the words we choose, where products are found via marketplace searches and found on search engines, but relying on that strategy alone is one that will take months if not years to bare any fruit. So self promoting is a must for most of us.
You can do this for free via almost all social media, through many blog sites, and even some websites can be built without spending a dime. It can be daunting to some to decide which social to use, or to start blogging, and to create a website... but to not utilize these tools will most likely mean that you will only receive limited sales.
There is always the chance that someone could buy your design on a product and make a video about it that goes viral and all the sudden your in the money... but you could just win the lottery too.
Start slow and find a social media that you are comfortable with. Stick with it on a consistent basis, as sales through promotion generally take a few months to start coming in. As you begin to experience success, learn from it and build on your success. That may mean joining another social, or starting a blog, etc. And spend some time learning about SEO and choosing good words in your title. tags, and description.
Best of luck with whatever path you choose, but know that this is not a get rich scheme and it does take a bit of effort outside of designing to be successful... 95% of the time at least...
or at least that's my experience... maybe someone else will chime in with theirs... that's way different...
Cheers
PC
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