How far were you off? That plays a big part in answering your questions.
I believe that throwing across your body can cause velocity, control, and health issues. First, as you mentioned, you will not get your hips fully squared up to your target and this means to me that you won't be fully utilizing your hip rotation. The result is a loss of velocity (although I believe it to be minimal) and, more importantly, more stress on the arm since you're not fully utilizing your body to throw with. Also, unless you're able to really open up your front foot and plant it so it's pointing to the target, you'll put more stress on the front hip, knee and ankle joints since your foot will be closed off yet your shoulders will still try to square up to the target and rotate around further than your lower body. In other words, you're gonna' twist up the front leg. This is wear and tear your body doesn't need.
Finally, there is a control issue depending on how far off to the closed side you stride. The issue is that even though the lower body strides off to the closed side, the upper body will still try to square up to the target. If it is able to do so via rotation only, then maybe this issue goes away. But the farther off you are, the harder it is to square up using shoulder rotation only. If you don't square up, then you risk health issues in the shoulder due to the shoulder being forced closer to a limit of its range of motion. But what often happens is that the torso bends sideways towards the target at the waste. This posture change can lead to a lack of control.
That doesn't make sense to me.
Yes. If you accept that the shoulders are going to try to square up to the target then, when you stride closed, the hips will stop short of being squared up. So, compared to how far the shoulders rotate, the hips don't rotate as far.
It goes back to my first question about how far off you were. I'm guessing it wasn't a lot. But that little bit might have actually worked out for you timing-wise. Of course, I can only speculate without seeing you pitch.
When I have a pitcher the strides closed only a little bit, the first adjustment I try it to just move them to the glove side of the rubber. This minimizes how much they have to "turn the corner" to get squared up to the target and increases the chance they can square up using only shoulder rotation.