No, is the answer and also the answer is 'yes'. Your question in the header is different to the one in the thread! A Q- colony does not simply stop. Usually, there is in the making, a new queen in a queen cell, or perhaps thirty or more, when the colony swarms and the queen leaves the colony. The existing brood needs feeding.
A hopelessly queenless colony will dwindle until death and so any foraging will be forlorn, but there may still be drone brood to feed because of laying workers' activities. That dwindling will take several weeks and possibly months to occur, the likely end being robbing of the weak colony in the late summer/autumn by wasps or other bees.
I have tens of years experience how queen is taken away for main yield during 2 weeks. Bees start to raise a new queen and brood rearinng ceases after one week and bees can concerate their all work to honey.
At same time you must have mating nucs where you get new queens to the hives.
In my climate when the queen lays at the first half of July, those bees do not forage neither winter. They are not needed. 2 weeks pause in laying is good, but 3 weeks is too long.