This kind of functionality is very compelling — especially if consumers can add even more detail and specificity — and could broadly impact online consumer behavior over time.
Eventually, I would expect all classifieds (and probably search) providers to offer this functionality. (A9 has something similar with Open Search.) Newpaper-owned ShopLocal.com also features alerts. Accordingly, product-specific alerts will probably also make it to shopping engines and major retailer sites (e.g., Best Buy). If the functionality penetrates that far and wide then people will do less "outbound" searching (this wouldn't affect product research) and more alerts/RSS provisioning.
Again, this functionality won't diminish the overall volume of searches but it may impact the how and where "ready to buy" consumers go to convert. This is a kind of parallel development to the so-called "verticalization" of search.
I may be overreaching, but the idea that I can plug in "2004 Honda Accord under $18,000" into a site and have results pushed to my email box is pretty interesting. I've told the site that I'm interested in cars matching those criteria, which makes me a more qualified lead than someone simply doing research on Honda Accords in a search engine.
One can already do this with jobs in Craigslist, CareerBuilder, Indeed.com and other jobs sites. Google, Yahoo! and others now have alerts for news and non-commercial search terms. I would expect them to promote this functionality more broadly in the future for shopping-related searches. Indeed, I would expect it to become almost ubiquitous within 12 months.