I haven't tested, but it
might count as gold. I already did it normally as gold, so... even if it
would count, I wouldn't know. Getting to that point with a new player file is a bit of a chore, unless I just Ctrl+F9 my way through.
Wow, this is a quick way to complete the level.
No, not really. Speedrun-wise, it's actually pretty slow, especially if you're going for all bonus coins. It does have the bonus of being able to skip the first room entirely (if you aren't going for all bonus coins), but then you still need literally all of the boxes. It might be slightly faster than the intended solution, but that's not saying much, because the intended solution is just that long.
The absolute fastest way I know of is this: first, you leave Peegue where he is. Then, you let Qookie collect everything in the first and second rooms. As soon as it's safe, Qookie enters the white TP and comes out below the box. Switch to Peegue, step left. Switch to Qookie, push box up. Switch to Peegue, push box right before the cannon kills you. Yes, this is possible, although pretty difficult.
The red/blue buttons never have to be opened because you can later go through the red TP and grab the last key that way.
Alternatively, if this is too tricky for you, you can have Qookie step
in front of the white TP, blocking it. Peegue then pushes his box to the right and stays on the teleporter. Then Qookie fills the water hole with a wooden box and pushes another wooden box through. Because of how this plan pans out, you don't have to do everything in one go, making it much safer than the faster method above.