With an upconverting DVD recorder, and a 32" LCD (720P) TV, is component cable adequate, or HDMI would give visible improvement?
Also, are component cables physically different from composite cables ( in specifications), other than the color of the plugs? I have lots of RCA cables lying around. Can they be used for composite or component cables?

Analog signal degredation is minimal over good component cables in common lengths (3-6 ft). So you shouldn't see a difference between component and HDMI. That being said, early HDTV designs were horribly inconsistent in their approach to handling HDMI. Sometimes, a DAC was used just downstream of the input so that older internals could be used that didn't support true digital sources. Thankfully, as new models come out, it's less and less likely that the internal design will have those old holdovers, but it's still a bit of a YMMV situation. Best advice is to beg or borrow both component and hdmi cables from a friend (or a store with a liberal return policy) and check it out with your particular setup.

Few, if any, consumer level composite cables are properly shielded to carry a component signal- it's better to get new ones. Don't worry, you don't have to pay $60 a set for Monster Cables like Best Buy and Frys want you to think. You can get good 5-cable (+audio) component cables for under $10 at monoprice.com. HDMI cables should be under $15 too.

I'll just add to the previous post, that you HAVE to try it and see. Given the variations between monitors and source hardware, it's not predictable and personal preference is always a factor. In theory, you should see more colors and a slightly sharper image with HDMI, but YMMV. Certainly, a 32" monitor is not going to strain either type connection to it's limits.