The short answer is, yes.
The long answer has a lot to do with glass breaking. The shorter version of the long answer is that if that stopper fit with an airtight stop the neck of your decanter would snap into pieces when you tried to pull that stopper out. Decanters are made for decanting, not for storing your top-shelf stuff for long periods of time. Decanters are designed to be temporary show vessels that also assist in aerating spirits that have been bottled up and need to breathe before being imbibed!
If you're feeling crafty you can probably add a rubber gasket to the "cork" end of the decanter, even then, you'll have to work pretty hard to get an airtight seal. If you're looking to store your distilled beverage of choice outside of the original bottle for an extended period of time, we'd recommend not using the decanter for that specific purpose.
As always, we're happy to help answer any questions, especially any questions involving whiskey. Hit us up at 866-902-7260.