Yes.
Many large corporations and organizations already operate on a global scale just fine. Just add some local and regional governments such as nearly all governments already do and you have a functioning global empire.
It is unlikely to happen with a democratic government without an alien invasion or some other reason to have world government but a fascist or communist government might go for world domination. Their legitimacy comes from a unifying ideology and works just as well (or badly) for a planet as it does for a single commune.
A theocratic government would also work. An Islamic caliphate for example would actually have perfectly valid reasons to seek to unite the world under its power. A Christian or Hindu version of the same would work just fine.
And manufacturing a reason for a democratic government to go for it isn't really that hard. Any kind of global event that threatens the extinction or subjugation of entire human species would work. Or people could just get really tired of pointless wars. The European Union largely exists because people figured that an economic union between France and Germany really would save lots of bother.
EDIT: Since I started by pointing out that corporations work on a global scale, I probably should mention that it has required some adaptations to how they operate. This is because the "working hours" happen at different times in different parts of the world. Typically (a simplified general model) you'd split the world into three operational zones (24/8 = 3) and have active operational control cycle between these. Typically these are the Americas, Europe and Africa (or EMEA), and Asia and Oceania.
A global empire would probably copy this solution and essentially have three administrative centers. Say, Washington, Brussels, and Beijing. Depends on how the empire came to be. The central government could be in one of these or cycle between them or even be divided between the three. The EU has split its functions between multiple locations for political reasons and it kind of works with fast travel and telecommunications.