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No.
Government should NOT – let me repeat that just so you can understand what I mean – NOT ever get involved in "price controls" because when any government tries to control anything they screw it up beyond all recognition!
Government controls = FUBAR
I think you misunderstand how price controls work.
This is not a debate question, it's a factual question.
If the price is set too high then naturally no shortage occurs. Most people are familiar with price controls working in situations of emergency when scarcity already exists in crucial supply-demand items and the prices are set too low to "prevent price gouging". But in fact, lots of price controls exist (or existed) which set prices very high and thus limited access to those who could afford it. Airline travel was done this way for decades through regulatory restrictions on what the prices would be. Long distance phone calls as well. Food subsidies used to work this way for decades as well (prices of corn or milk or sugar are or were basically set by the government). In none of these cases was there a shortage.
The actual debate should be something like "are price controls necessary?" because most of the time they have very little to do with controlling supply and have more to do with extracting rents from the economy. (ie, they're unnecessary, this includes anti-price gouging laws).
I think the assumption has to be made that this refers to a necessity. I mean a shortage for a non-essential is based around more people wanting to buy at the price point than there are models / items to be purchased, so price controls (which invariable raise the price of goods) cannot create a shortage for non-essentials. But because a shortage in essentials can be defined around access to them regardless of price point (not saying it should be, but it can be), I must assume that's what this question is referring to.
This is a vaguely worded question referring to a very specific set of circumstances then. "Price controls" refers to all manner of government price interferences, not simply price gouging laws.
So if this particular scenario is the actual question, I'd probably be willing to argue that the cause of a shortage of "essential" goods, particularly in times of crisis like we might be describing here, has less to do with the prices then and more to do with a sudden and severe demand shock upward. The use of price controls at that time simply speed up the shortage rather than cause one, by depressing the price on the legal market. Elastic price consumption would tend to use up all goods regardless of price if they are essential goods.