I think it's possible for such empire to exist within a solar system. I would say that having both military might and control of information is the key of creating such a huge empire.
Right now, we can say China's CCP could be a prime example of a modern empire. They have very strict control of information. No privacy is given, as they're required to have their actual ID to be able to access online. So if someone wanted to say something bad about the government, they know who it was. Not only that, propaganda is everywhere, as China's government also controls the TV networks and newspapers. They can always point their flaws to the enemy, and without any comparison with other media, will believe that it is true.
Undeniably, having a huge military force would be an essential factor to have control of the empire's citizens. The empire needs an organization to enforce the rules that it has, and the military would be the best for that. Coupled with controlling information, and the emperor can just bring down any of its citizens due to [insert false info here].
To be a living God may not fully work in a futuristic setting. With instant communication and surveillance, any emperor or it's family being treated as divine beings will be monitored continuously throughout their lives. 752
Any flaws or mistakes will be pointed out by the masses, and at the end of the day, recognize them as any other human being. So unless an emperor lives for a huge lifespan that no other humans can achieve, I doubt it is possible.
Communication is definitely a factor, though with an interplanetary setting, it may not be a huge one. For example, it will take about 43 minutes for a radio transmission to be sent from Earth to let's say Jupiter (Europa is a possible moon to colonize). While not instantaneous, we've survived longer delays in communication back in the 90s (Cuban Missile Crisis, negotiations between US & Soviet Union), so adjustments can definitely be made. Besides, with a huge military might, there will be stations in every major colony to "keep the peace".
Transportation on the other hand, is a bigger problem. Colonized planets could or must be self-sufficient that it produces it's own food and resources, rather than being depended on a "farming planet", unless technology has reached the point where it only takes days or weeks to arrive on another planet instead of years. At that point, very specialized planets would arise. Would be cool to see an industrial planet with a huge hole at the center, as it is being used to construct massive spaceships at the very center, and launch them once done. Or, a planet rich with heavy metals being surrounded by harvesters, eating the planet bit by bit and have a network of ships going back and forth, delivering said harvest to other planets.
Probably a big way for an interplanetary empire to form is to have a common goal.. or enemy. What if there's another empire or colony threatening the lives of the solar system? Humanity will likely band together to fight a common enemy and will voluntary join a part of an empire that will guarantee their safety. 99