Will pre-oiled vegetables become soggy?
It will definitely change some vegetables, specifically tender vegetables with large surface area (e.g. whole leaf ones). Have you ever tried making a complete salad including dressing, then storing the leftovers in the fridge for a day and having it limp the next day? That effect is due to oil. 

The mechanism behind that has nothing to do with penetrating the vegetables or having the oil soak into them. It is just that it stops their perspiration, so they die off earlier than they should. (I know it is counterintuitive, but metabolically speaking, your raw vegetables are still alive in your fridge). 

So I wouldn't describe the change as getting "soggy", especially because some kinds of vegetables won't change that much anyway. Especially those which are fruits or roots or tubers will stay mostly firm even when oiled. But e.g. spinach will be definitely different - whether you care for that difference or not is up to you.