In most cases, it won't make any difference as far as upscaling is concerned. HDMI is just a digital data connection, it doesn't do any upscaling, so you would need a scaler as well (which would already have an HDMI output on it, anyway).
You need something that takes Component Video at SD resolution and upscales it to HD, then takes audio (analog or digital) and merges it with the digital video to create an HDMI output. Something like:
http://www.antonline.com/p_AT-HD510VGA-NX_576557.htm
There aren't too many of them out there and they cost more than even a really good upscaling DVD player (Oppo, for example).
But your TV already upscales any signal to the native resolution of the display and you would still need to connect the 5 cables up between the DVD player and the scaler, so unless your HDTV doesn't have any Component Video inputs left, there would really be no point in doing this. Even then, it would be cheaper and simpler to just get a Component Video switch box.
If you're worried that a new upscaling DVD player won't be as good as your old DVD player, as long as you stay away from the cheapest stuff, like CyberHome, Apex and other brands you never heard of until a few years ago, you will probably be fine.