Yes, if you endanger others
In Finland, the traffic law (Finnish text) defines users of mobility assisting devices as pedestrians.
However, the criminal code (Finnish, or out-dated English translation), chapter 23, section 9, defines a crime called "Non-motor powered traffic intoxication":
A road user who operates a non-motor powered vehicle under the influence of alcohol or other narcotic substances, thereby causing a hazard to others, shall be sentenced for non-motor powered traffic intoxication to a fine or to imprisonment for at most three months. [emphasis added]
This is the crime that applies to e.g. bicycles as well. That old version doesn't specify which vehicles count here, but the current text is more explicit, and also includes mobility assisting devices with at most a 1 kW engine and 15 km/h max speed.
They key part is "causing a hazard to others"; just being drunk shouldn't be enough.