Good question about CafePress. You can certainly do it, but you will definitely pay a lot more, in some cases twice as much. And if you want to have the items shipped from the manufacturer out to, say 100 individuals at different addresses, I would guess that CafePress will not be set up to do that.
The appeal of using CafePress (or the less-known Zazzle.com), of course, is the ability to instantly view your product onscreen, and complete the whole process right on your desktop. Most other sites that do this (such as www.corporatecasuals.com or www.hanesbullseye.com) charge a one-time setup fee of around $65 if you want to upload a logo.
So in conclusion, CafePress is a convenient option if you're doing a small volume, but the difference in price will add up quickly.