Yes. Of course it will. If anything, it will make them stronger, as they are currently all together, "fighting" the same common enemy, strengthening bonds.
It doesn't need to be about handouts. It's also about sharing. Resources, expertise, buying power. Yes, it may need to change, and yes, that might mean that some decide to leave (because they were in it for the wrong reasons in the first place), but that might/would make the EU stronger.
Will we join the EU programme to procure ventilators? Who knows. At the moment, we haven't, apparently. I'm sure there's some "logic" for that, but I'm buggered if I can think of it.
ASEAN works. The USA works. Hell, even a Farmers' co-operative works. The EU was working too.
In my opinion of course.