If it happened overnight - perhaps.

But the algorithms behind Bitcoin are agreed on literally by consensus, the clients in the network which reach a majority are in control.

If it became clear that something in Bitcoin was about to be broken, the algorithm could be changed to something more secure, if a majority agreed.

Past transactions would not be affected - they are immutable - and new ones would become safe.

It would also depend on the economics of said quantum computing. But yes, I'd expect the value to decline because one could not guarantee their currency anymore. Similarly if someone invented a teleporter that targeted US currency, it'd become worthless because a thief could just teleport it out of your pocket.