The short answer is, yes.
The long answer has a lot to do with glass breaking and liquid evaporating. The shorter version of the long answer is that if that stopper fit with an airtight seal the neck of your decanter would break into pieces when you tried to pull that stopper out.
Also, decanters are made for decanting (pouring), not for storing your top-shelf stuff for long periods of time, liquor will evaporate when left outside of a bottle with an airtight seal. 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 and the wobble drives you crazy you can probably add a rubber gasket to the "cork" end of the decanter to stabilize it, even then, you won't be able to get an airtight storage 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 a 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.