There are two paid promotions with no answers required. They are "ファンイベントのお仕事" and "地方TVCMのお仕事". Just select the correct region, and you get a free Perfect Communication. However, these don't show up until late game to balance it out.
Not entirely correct - The 'non answer' paid promotions can show up early, although the odds of it showing up first thing are nearly zero. See the last paragraph for how early this can happen.
You can only do an answered paid promotion once.
You can however, do unanswered promotions multiple times. Never seen a poor one, but I suspect this has to do with your idols' mood level.
It doesn't happen too often, although in hyper mode, it happens more often than not, surprisingly (since you live and breath paid promotions as a method of training up your image level while maintaining fan count) and since it isn't actually uncommon for a hyper run to have just two performaces in a 10 week period, (namely, 4 weeks of promotion and lessons, performance to score, then another 5 weeks of promotion and lessons) and there's only 12 promotional events, you can probably can guess what's going to happen.
Due to that setup, it isn't actually THAT abnormal to see image level 8 or 9 before the 10th week, either. I've successfully closed out on S rank Hyper mode image level 16 by week 27 or so.
My games extensively use paid promotional events in Hyper mode, mostly as a method of destroying the competition via an abnormal buildup of fans. the number of fans, as well as the full reversal of fan mood make it a useful tool, if very expensive to deploy.
