You should use pickling when you want something to last months not days.
In regards to your second question: it certainly wouldn't be pasta salad any more.
If you want to experiment with pasta pickle then sure it sounds like a good idea, if you want to preserve pasta for a week split it into several air tight containers and stick it in the fridge.
Penne or fusilli work well in pasta salads. The key to cooking pasta well is:
Use as big a pan as possible, with plenty of water, to dilute the starch that comes out of the pasta.
Add plenty of salt - a good couple of tablespoons of sea salt, more for a big pan.
Get the water to a proper rolling boil, add the pasta, stir, put the lid on the pan to get it up to the boil again quickly. There is no need to add oil if you do this.
Cook the pasta as per packet instructions, but check it a couple of minutes before it should be ready. You want it to have a bit of bite, not be totally soft.
Get your dressing onto the pasta ASAP to prevent it from drying out, and drizzle with good olive oil to help it last longer.
My answer would be "not at all". My pasta salad involves only raw vegetables - carrots, peppers, celery, and similar things you would put in a leaf salad. The contrast between the soft pasta and the crunchy veggies is part of the appeal. Just a data point.
Best Answer
You should use pickling when you want something to last months not days.
In regards to your second question: it certainly wouldn't be pasta salad any more.
If you want to experiment with pasta pickle then sure it sounds like a good idea, if you want to preserve pasta for a week split it into several air tight containers and stick it in the fridge.