Thanks for your question; we get quite a few along similar lines.
As you have an SD TV, it would be a waste of money to upgrade to an HD STB, as no matter what, the output will not be higher than what the set is capable of producing. As standard definition set top boxes produce interlaced signals only (576i), some people claim that you will see a difference with an HD STB if your plasma is capable of handling progressive scanned inputs (e.g. 480p, 576p), but unless you have a very discerning eye, we doubt you will be able to tell the difference.
The reverse is somewhat true -- HD sets will upscale a standard definition input, but that will always result in a close approximation, not a true HD signal. The picture quality will be dependent on the capability of the TV's image processor.
An HD STB will also give you Dolby 2.0 and 5.1 audio, which would be a benefit for those few programs that are broadcast with surround sound, but of course you'd need to be hooked up to more than the set's two channel speakers as well.
As you note your plasma has an HDMI port, you may get a better picture by making sure you're using it -- so a new STB with HDMI out may be worth your while, as you will probably notice an improvement with an all digital signal.