If all people on earth would gather in and around one city and we'd switch off all the lights, would all people be able to see all stars that are visible with the naked eye simultaneously?

No, lots of reasons not. Biggest reason is a majority of the stars will be below the horizon and seen from the other side of the earth, the side where all of those people just came from.

At any point in time half the stars are visible from any point on the earth (the other half being below the horizon). And if you live in the northern hemisphere there are certain stars located in the southern part of the celestial sphere that will never rise above the horizon (conversely, for a resident of the southern hemisphere there are stars in the northern half of the celestial sphere that they never see). To see ALL the stars you either need to (a) move some place where there is no horizon - such as in space, or (b) move to the earth's equator so that you can see both northern and southern hemisphere stars simultaneously, and theoretically if you watch from sunset through sunrise the next morning you should be able to see all the stars at some point during the evening (assuming you have a clear view all the way down to the horizon in all directions).