As a techno numpty myself but I would say it wouldn't. If it is recorded as a standard dvd then it would not have the required amount of pixels to make it HD 
If you Google it standard pixel rating is 480p whereas HD is 720p
Standard UK DVD specs for region 2 (UK) are typically 720x576 pixels (PAL).
In USA they will have 720x480 pixels (NTSC).
What exactly is it upscaling then?
If the disc you're playing isn't 4K, your blu-ray player will upscale it. An algorithm is used to fill in the gaps between the quality of the source material and what a 4K version would be, and the best 4K players should do a job of this.
It's likely your 4K TV will have a similar 'engine' that generates, (upscales), from a lesser source to fill the screen.
Other things to mention (if you want to research) are interlaced/progressive, Aspect Ratios (see below), Non Square pixels, Chroma Subsampling: 4:4:4 vs 4:2:2 vs 4:2:0. Bored yet?
As you can appreciate, there's a lot of images (per second) being created on the fly but processing power shouldn't be a problem in such dedicated players; it will boil down to how good the algorithm is as to the actual quality of the output.
Advanced Aspect Ratios - PAR, DAR and SAR -
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