- Is this correct?
Probably. Your presence in Italy is permitted because of the pending application for the permit. But you have no basis to be in other Schengen countries after you have exhausted the 90-day visa-free limit for short visits.
However, if you have a type-D visa issued by Italy, then any days you spend in Italy during the validity of that visa do not count towards the 90-day limit. If you haven't exhausted the 90-day limit, then the only thing preventing you from going to other Schengen countries would be Italian national law.
I do not know what Italian national law says about that, but countries sometimes consider that if you leave the country you have abandoned your residence permit application. That question is rather more on topic for Expatriates than here.
- What will happen if I travel within the Schengen area and am checked without my permit to stay?
It depends on the national law in the country where you are checked, as well as on the personal discretion of the officer who checks you. Worst case, you could be deported. This is probably extremely unlikely. Other possibilities include being
- sent to Italy
- told to go to Italy
- allowed to go on your way
Some will point out that in some countries, officers do not have personal discretion over these matters, and while that may be true as a matter of law, there is never anything that stops an officer from letting you go.
My experience with Swiss authorities, however, is that they are relatively stricter about adhering to the law than those in other countries, but even still, you might be lucky. (For example, I once left the Schengen area from a Swiss airport, and my traveling companion had not received an entry stamp when we had come in through the land border. The officer said that he should fine her, but he did not.)
So you will probably be fine, but I wouldn't risk it unless there were some compelling reason to do so.