No. The main reason for this would be a simple fact that throughout the Antiquity and Early Middle Ages, there was no distilled alcoholic drinks in the entire Europe and North Africa, and te first grain distillates started to appear only in the very end of the medieval period.

Although process of distillation has been used since 18th century BCE in Mesopotamia and Egypt during the production of perfumes and medicines from essential oils and rosins (although it is worth noting that such usage of the term 'distillation' conflates typical distilling process and pyrolysis sometimes called 'dry distillation'), it was not used in the production of alcohols meant for any kind of consumption (medicinal or recreational) until roughly 8th century AD. Even then, it has been used to create highly concentrated alcohol solutions using wine as the sole material, what will change only in 15th century or late 14th century at the very earliest.

The first documented mentions of alcohol distillation come from the first half of 9th century AD, being mentioned Jabir ibn-Hayyan's Kitab ikhraj ma fi al-quwwa ila al-fi`l [Book of obtaining power necessary to the action], and the Kitab al-taraffuq fi al-‘itr [Book on the delicacy of perfume] by Yusuf al-Kindi, court physician of Harun al-Rashid, caliph of Bagdad, where it is a result of wine distillation, technically making this substance a brandy (the English word 'brandy' comes from German 'brandwein' meaning 'burnt wine'). In the original text of ibn-Hayyan it was called 'araq, literally 'sweat' or 'perspirate', possibly after the droplets of the condensate forming near the alembic's outlet (hence arak, a contemporary Middle-Eastern distilled drink made of dates or grapes with which Turkish raki and Balkan rakiya share the etymology). It is worth noting that this work gained popularity only somewhere in 10th century, as until that time, the term ma'sid hamr (lit. elevated wine) was more common. Distillation most likely appeared in Europe in the late 11th century, as evidenced by the texts associated with the Medical School of Salerno, very possibly thanks to the contacts with the Arabic world from where medicine and natural sciences have been developed over last few centuries.

Beer was also not that popular among Romans. In the Roman Empire (and Republic), wine was the most common drink thanks to the ubiquity of the vineyards. Of course, the quality varied heavily and the drink of a lowly plebeian was quite different from the one enjoyed by patricians, but from technical perspective it was the same product of grape fermentation. In the Empire era, beer, popular among the inhabitants of Gaul and Germania found its way to the Roman world, although its reception was rather limited. It is worth noting that the drinks similar to beer were also made in Greece, although it is possible that they were more similar to modern kvas, as e.g. Zosimus of Panopolis in 4th century wrote that the brythos and zuthos were drinks made from malted grain and malted loaves respectively, that were later fermented and strained rather than brewed. There is a notion, however, that lack of a consistent terminology for beer or a class of drinks made of malted grain in Greek or Latin (the aforementioned two terms were generally applied to beverages made by Thracians and Egyptians respectively) suggests little interest in this particular drink. On the other hand, practice of using the term 'vinum' in Latin to designate various products, as indicated by e.g. Masurius Sabinus in 1st century AD who noticed that the term 'vinum' might also apply to vinegar and zythum or camum, with the two later term being generally understood as types of beer. This is largely reflected in Greek, where aforementioned Egyptian zythos is often referred to as 'barley wine' (o ek kriphes oinos) by e.g. Herodotus, Xenophon or Theophastus (5th-4th century BC), but also later authors, such as Dio of Alexandria (1st century AD), suggesting that the proper terms and generic 'grain wine' could have been used as synonyms. Nevertheless, even taking all of this in consideration, references to beer or other grain-based beverages are far less common than references to various forms of wine, at least in the core lands of the Roman Empire.

The existence of the alcoholic drinks being produced from grain in the Northern Europe is generally attested as early as 1490s, One of the earliest such documents is the ledger containing an order of 'eight bolls of malt to Friar John Cor wherewith to make aqua vitae' written in the 1494. A record written by High Treasurer of Scotland in 1498 that speaks of the payment of '9 shillings to a barber who brought aqua vitae to the king in Dundee' is also often cited in this context, although it is not certain whether the aqua vitae referred to grain distillate or wine-based distillate, possibly made for medicinal purposes. This would mark Ireland or Scotland as a very possible birthplace of the grain alcohol, as virtually all recipes for strong drinks (usually medicines using strong alcohol as a base) from continental Europe written until early 16th century speak of the distilled wine as the basic ingredient. There are some notions that the alcoholic drinks were made from rye by a Russian Orthodox monk Isidor, who has visited Florence and then created a rye mash distillate in early 1440s, although this is largely considered a legend, possibly related to the fact that the distilled alcohols most likely arrived in Muscovy in 1429, brought to the court of Vasily II by the Florentinian and Genovese envoys. Nevertheless, the first production of the grain alcohol we know of dates back to the 15th century at the very earliest.

So, to sum it up, Roman spectators of the chariot races would not be able to drink strong alcohol obtained through distillation, because such process has not been in use yet and was likely completely unknown at the time. So were the people at the court of Charlemagne. People watching medieval tournaments would also have to resort to wine and beer, as distillation, already known in Europe was used chiefly for medicines rather than recreational drinks. Only in the very last century of the medieval era humble grain and fruits became the basis for the strongest alcoholic drinks around.