I really doubt that. Look at how people were behaving until the day the lockdowns began. Look at how people are behaving now. They aren't afraid of going to bars and restaurants and shops. There is no good reason to believe that they wouldn't have behaved the same way the entire time, if the lockdowns had not intervened.
It's obviously true that the economy would have been damaged with or without the lockdowns. It's entirely different to claim that the damage without lockdowns would have been as bad as the damage with lockdowns.
Again, it's not like the economy would not have been damaged either way, but it's obvious that the lockdowns made the economic damage worse.
I also doubt it and wouldn't argue it myself, I was just pointing out that making that argument need not imply that you think there are no other costs, i.e. those arguments are not equivalent.