Yes, the fact that the lictors' rods (lat. fasces) appear as the symbol and the namesake of the Italian fascist party and found its way on the American coin is pure coincidence. First and foremost, this particular coin has been designed and introduced in 1916, while Italian Fasci di Combattimento were created by Benito Mussolini as the veterans' organization in 1919, while the Italian Fascist Party was founded two years later, in 1921. This symbol, hailing back to the Etruscan period, was most commonly associated with the ancient Rome, especially its republican period and was adopted by Italian fascists as the symbol of unity, state power and 'glory of Rome' Mussolini wanted to revive. But they were pretty late adopters, so to speak.

In general, a bundle of rods were a symbol of the lictors, essentially bodyguards, representatives and closest associates to various Roman officials and thus were closely associated with the administrative power or the state in general. In addition, due to their shape, they became also a symbol of 'strength through unity', a common idea within Western European and American republican movements that gained more and more popularity since late 18th century.

In the capacity of the judicial or punitive power of the state, fasces with an axe can be found on the seals of emblems of US Tax Court and National Sheriffs Association, US Courts Administrative Office, US Army Reserve Legal Command or State Seal of Colorado, while two crossed fasces are depicted on the insignia of the National Guard Bureau and US Senate. They are also common symbol adorning various courthouses and administrative buildings that sport classicaly-inspired decorations and are also present as a symbol of state power in various policing or administrative organizations, such as Spanish Guardia Civil, police force in Sweden and Norway, military police in Mexican and Ukrainian Army or Federal Bailiff Service and Federal Service for Supervision in Education and Science of Russia.

As a symbol of republican unity, lictors' rods are prominently displayed in the coats of arms of France, a tradition that hails back to the first Great Coat of Arms of the Republic designed in 1792. Although not official and since 1870 not defined in any legal text, they were widely known and used nevertheless. They were also frequently changed, although fasces were and are a central or prominent element, as opposed to coats of arms of French Empire and Kingdom after the Bourbon Restoration. In addition, fasces with a spear and Phrygian cap are presented in the Jean-Jacques le Barbier's 1789 illustration Declaration of the Rights of Man and the Citizen. It is also present on coat of arms of Cameroon, Cuba (and its provinces of Camaguey and Artemisa), Equador and Gran Colombia, as well as St. Gallen canton in Switzerland and several municipalities in Germany and France. They can be also found on e.g. Diggers' flag of the Red Ribbon Rebellion that took place in Australia in 1853, as well as in the emblems of Chi Phi Fraternity founded in 1824 and Alpha Phi Delta Fraternity, founded in 1914. In all these usages, rods represent unity.

Thus, the lictors' rods were a common symbol associated with republican government or societal cooperation in general, and was quite often used in European and American republics since the late 18th century onwards, thus its usage on an American coin should not be a surprise.