getting his morphine drip topped off

[Ostap]

"Can you imagine what things would be like with Donald Trump at the helm right now? I mean, put aside everything else, have you heard him talk lately? He sounds like he's muttering to himself while sitting under his favorite tree at the old folks' home, after getting his morphine drip topped off."
link with timecode Late Night with Seth Meyers

Hello, am I right that it means after his morphine drip was refilled (and now it is full)?

 

[probus]

You are probably right, but it's not very important to the joke. In addition to relieving pain, morphine makes people sluggish and stupid.