Yeah, that's pretty much how our Affiliate program works, in that our Affiliate links set a cookie good for 6 months (or whenever the prospect or their browser deletes their cookies!), so any Affiliate-eligible product that prospect purchases from your site within the next 6 months would tell the E-junkie cart to calculate a percentage back to the originally-referring Affiliate.
Affiliate links are configured on a per-product basis, so the Affiliate link codes we offer are "for" that particular product; however, each Affiliate "Hop Link" sends a user to whatever URL you specify, so you could just setup your Hop Links to point to your homepage or to any other page you choose on your site.