A pickle that would preserve it for a week?
Would it ruin the taste of the pasta salad?
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.