No. I've seen some experiments with MIG machines welding, but it really isn't possible to do well or right as is. Keeping it simple, it is because MIG uses a constant voltage power source, and stick a constant current power source. These are the names given as they loosely describe what is happening while the power source is operating. There are changes in voltage in MIG, and current in stick, but these changes are minimal compared to the changes in amps while MIG welding and volts while stick welding. Basically, voltage goes down the closer the arc is held while stick welding. In MIG, the amperage is controlled by the wire feed speed, but it falls when the wire touches the puddle.
Anyway a unit has to be designed to perform both type processes, though a stick unit can be used to power a voltage sensing wire feeder. Shield Arc can tell you all about those.
Stick has its advantages and MIG has its. To say one is better than the other is like saying Fried Chicken is better than Fried Fish to a Southerner.
Stick may be more versatile than MIG in the fact that it can be taken almost anywhere to weld in a compact package almost any common metal or it can be the main process of an engine driven machine capable of producing hundreds of amps, but MIG itself, in the shop is a more productive performer.
