No.

The modern definition of "Empire" is generally understood to mean a monarchy that unites, willingly or unwillingly, multiple nations (e.g. two or more Kingdoms). However, historically the word "Empire" has had many different definitions: the ancient Romans, who invented the term, defined Imperium as legal definition of all that which was under the control of the Magistrates during the Republican period, and later all that which was governed by the Principes. The title of Imperator, on the other hand, was originally a military honorific given to victorious generals, which was only later appropriated by the Principes, in modern parlance referred to as "Emperors."

So when you see historians talking about "Empires" prior to the Roman Empire or outside of Western Europe, they are generally using the generic definition to denote a monarchy governing a large, multi-ethnic territory, or a monarchy that has united multiple previously disunited political actors (like the Egyptian Empire uniting the Upper and Lower Egyptian Kingdoms, or the Chinese Empire uniting the disunited Chinese Kingdom).

After evaporation of the western half of the Roman Empire, the term "Emperor" continued to be used to denote the ruler of the East as it had been in previous centuries, even though the empire was largely (but not solely) ethnically and linguistically Greek. In Western Europe, the word Emperor was revived by the Pope Leo III in the eight century by crowning Charlemagne the title. The legal meaning of the word at this point in time is interesting. It's important to note an often overlooked but unsurprising aspect of the Empire in the East: its retention of a number of longstanding Roman legal constructs, including the "civilizing mission" of the Imperium. For the ancient Roman legal scholars, the Imperium had no borders, just frontiers past which they had not yet imparted civilization and rule of law. So although Pope Leo III used the title "Emperor" to prop up the legal justification for Charlemagne's ultimate authority over his "Empire" by drawing a connection from Charles to the old Roman Emperors, this understandably peeved the existing Emperor in the East, whose empire retained two large military provinces in Italy and would, resources permitting, like to reaffirm itself on the mediterranean basin (although an unrealistic aspiration, this didn't stop Justinian in the sixth century).

It is under the Carolingian dynasty's rule over Western Europe that the modern notion of "Empire" emerged: the Carolingian system allowed for the existence of individual monarchs in Italy, West Francia (modern France), and East Francia (modern Germany) working under the assumption that one of the three would rule over the others as "Emperor." Understandably, the system was less than perfect and broke down quickly, leading to the emergence of distinct French, German, and Italian nations. Of the three internal divisions of the Carolingian Empire, only the western one (France) developed a unified central monarchy, while Germany and Italy slowly fragmented into distinct polities with fluctuating degrees of unity under the construct of an "Empire," further reinforcing the notion that "Emperor" is a supra-monarchal office.

By the time Napoleon rolled around and conquered most of Europe, he also appropriated the title "Emperor" for himself, crowned by the Pope no less. In part, this was done to distance himself from the unpopular French monarchy deposed by the Revolution, but it was also done to invoke the prestige of the old Roman Empire and signify his dynasty's hegemony over all the disparate nations of continental Western Europe (he not only expanded France's national territory, but propped up his relatives as monarchs of Spain, Naples, and Tuscany, while also crowning himself King of Italy).

After Napoleon, the title of emperor was appropriated by a number of Monarchs to signify their rule over large territories and different peoples: Napoleon's nephew, Napoleon III, following France's reinstitution of a Monarchy only to again revert to a Republic, elevated himself to "Emperor" from the office of President to signal France's return to greatness and emphasize his success in expanding France's colonial empire (a bit of a stretch, but Napoleon III was also invoking his uncle's legacy). Upon the fall of the Second French Empire at the hands of the Kingdom of Prussia in 1871, the seemingly unstoppable Prussians managed to get the minor German states to accept a united, "German Empire" where the german rulers retained their titles and territories, but were now under the umbrella of an Emperor (the stunt also had the intent of signaling to the Germans' intent to supplant France as the dominant power in Western Europe). Not ones to be outmatched, the Brits under Prime Minister Benjamin Disraeli worked to elevate Queen Victoria's titles to include, "Empress of India" in 1874 with the excuse of signaling the United Kingdom's rule over the previously disunited Indian "Princely States," in addition to officially titling its sprawling possessions all over the world the "British Empire."

In the modern era, the term is also very often used figuratively: for example, the United States created a number of international institutions after the Second World War like the WTO, IMF, and UN. The willingness of many countries to join and participate in these institutions led some political commentators to call the United States an "Empire by Invitation."