Awful is 3, Inept is 4. Yes it's important since it will improve performance in games, especially if you don't have a very strong bench. It also helps maintain gameshape, so training it to around 7 should be worth it in weeks where you only have 2 games like this one.
Like said, trainer level doesn't influence speed of stamina/FT.
I'd say unless you have 18/19 year old guards that are at least 6'4", I wouldn't train IS if it's at atrocious. It takes very long to train and it will need several pops before it makes a difference. Unless they're All star or lower potential, then you have enough time to cap them.