Such a DVD player contains a scaler, which up-converts the 480i DVD content to one of the HD resolutions (i.e., either 720p or 1080i). Depending on your DVD player and its setup, your monitor and its setup, and the connection type between your DVD player and the monitor, it may or may not affect the Aspect Ratio (i.e., 4X3 versus 16X9). Upscaling resolution and changing Aspect Ratio are somewhat independent functions.
The DVD Players with scalers that I know of require a DVI or HDMI connector to utilize the upscaling feature, but there may be some that can do it with other connections.
"...is it really going to be HD quality?", well not quite. If properly set up with a fixed pixel monitor and a DVI or HDMI connection, the PQ will be better than any other DVD PQ currently available, but it isn't true HD. All you have to do is watch HDNET or DISHD and the difference is rather obvious.
The bottom line is you need to read the manuals for the DVD player in which you are interested and for your monitor. Those will give you the setup requirements and the limitations by setup that apply.