Doubtful. Just think about the toilet paper shortage; a common household item that never would have had a supply shortage if people just maintained their regular buying patterns.
Now think of masks; a non-household item that a small percentage of households carried. Even if people were reasonable and only bought an amount to cover their needs, that would have introduced hundreds of millions of new buyers for that item.
There would have been a supply shortage even if people just maintained their regular buying patterns, simply because they started to use their home toilets much more and their business toilets much less, and those are different products (sometimes literally physically incompatible with the holders) with different supply chains, so an unexpected switch from people using product A to product B is inevitably going to cause a supply shock.
Solution, be honest: "Masks work, but we don't have enough and need them for hospitals so you're not allowed to buy any. Wrap a tshirt around your face instead, it's probably better than nothing."
Huh come to think of it, banning the sale of masks would have been the most brilliant strategy to get people wearing masks.
Imagine if instead of putting out a press release, they had quietly banned selling masks by retailers and then 3 days later when people caught wind of it explained the shortage mean they were only for hospital workers.
All the anti government reactionaries that are now anti-maskers would be the most ardent mask wearers.
Now think of masks; a non-household item that a small percentage of households carried. Even if people were reasonable and only bought an amount to cover their needs, that would have introduced hundreds of millions of new buyers for that item.