Since I can't find any information anywhere on load time differences, I will be creating the information. Because I am completely new to speedrunning this game, I will test the loading times of my GameCube with and without a memory card and my Wii with and without a memory card. Keep in mind that there are different versions of both consoles I'm testing on so your results may vary. If this game is anything like WindWaker then I expect the GameCube load times will be faster.
For my own convenience, I'm timing the loading screen of Offensive Driving 101 stage 1.
Wii without Memory Card: 6.43s 5.40s 6.71s 5.96s 6.38s 6.35s 6.36s 6.41s 6.18s 5.90s Average: 6.208s
Wii with Memory Card: 5.26s 6.48s 5.93s 6.48s 5.85s 5.93s 6.60s 5.85s 5.85s (cool) 6.39s Average: 6.062
So it would appear that load times are magically improved by having a memory card with a save file on it but this is (A) more than likely too small of a sample size and (B) more than likely mute because of extra text boxes and inputs due to the presence of a memory card or lack thereof. This is all of the timing I can do at the moment, GCN timings are coming soon.
Eureka! When you don't have the memory card in, there is no autosaving! Autosaves seem to take about a second after each event which will really add up over a run. The game still prompts you to save your name when you break a record after an event but that's only one extra input and negligible extra time.
I'm finally around my GameCube to do some testing so here goes:
GameCube without Memory card: 5.83s 6.66s 7.03s 6.98s 6.60s 7.00s 7.13s 6.63s 6.20s 6.58s Average: 6.664s
GameCube with Memory Card: 5.73s 6.70s 6.66s 6.98s 7.18s 6.66s 7.16s 7.33s 6.45s 6.45s Average: 6.73s
These times are much less consistent but slower nonetheless. It doesn't really matter to me because i can get better quality out of the wii and it's easier to capture but someone out there might care.