It's actually the opposite. Just look at France. They are massively overproducing most of the time, even when they run checkups and maintenance on a lot of their plants in summer, they have huge amounts to export. And yet they still need imports in the coldest weeks of winter (while even winter on average sees overproduction).

So no, nuclear countries will not sell any power in times of shortage. They will be the ones needing imports from countries with storage. Or they need to start up storage themselves, too. Because enough nuclear base load to survive the few weeks with high demand without imports or storage when your renewable half of production is underperforming is insanely expensive. As it means having a lot of overproduction the rest of the time... but with no market to export anymore like they have today, because all countries will have high demand and low supply in the same time frames.

(Speaking about France: Their grid provider ran a big study about future electricity production. And the only reason nuclear (even more than the minimal required base load) was economically viable was because they plan with hydrogen production all year. For industry, for export (because -as I said- they need a way to export when not everyone has high production but low demand) and as storage...)

PS: Yes, the conclusion is that nuclear needs storage to be economicaslly viable. Just like they need a lot of complementing renewables. But don't tell that to the nuclear cult pretending storage is impossible and renewables don't work, because their heads might explode. Wait... Do tell it to them, as these exploding heads would be an improvement.