What would be the load time differences if the HDD is used instead of disc?

So this has yet to be tested, however I can't imagine the load time difference will be too noticeable as Xbox already has fastest load times by a significant enough margin, as it's loads, while not instant, might as well be in comparison to the other versions.

If you do plan to run on the game loaded from an HDD though it would fall under emulation guidelines.

https://www.speedrun.com/pmw2/thread/og710 This post outlines the ruleset, and reasons. Basically these runs are allowed but if you use emulation/boot methods other than the original disc, after a certain time your runs wont be verified till you play on an actual disc.