It seems remarkable that a four-year old boy would be sent so far, with the most direct land route being around 1,200 miles. Charlemagne's legacy must presumably have included a safer route, but even so!
And the Brut Y Tywysogion (Welsh: Chronicle of the Princes) reveals that Cyngen, who was King of Powys (i.e. one of the neighbouring kingdoms to Wessex) died in Rome in 854CE, which is the year after Alfred's arrival, although doesn't go into detail. Did the Romans keep records of all these high profile visitors to their city and what they got up to during their stay?
(EDIT: typo)
Not completely relevant but I can provide a couple of additional details concerning Alfred's trip to Rome.
The route taken was called the via francigena which was a series of paths that ultimately led to Rome. For Alfred's party there were "some eighty stages, with each stage requiring a journey of approximately thirteen to fifteen miles." The route is described as treacherous due to Danish raiding parties on the Frankish rivers in addition to bandits that would attack pilgrims on the road for easy targets.
A system of inns, churches, and monasteries provided traveling parties with whatever needs they had. A hostel in the Italian town of Brescia actually maintained a record of all who stayed with them, which includes a surviving signature of one "Alfred" among its ninth-century Anglo-Saxon guests.
By the time Alfred arrived in Rome for the first time Pope Leo IV had ordered and completed new fortifications and defensive walls to protect the city and its visitors from Saracens who had raided the Bascilica in 846 A.D. Within the city was a community of Anglo-Saxons that worked and lived in the city known as the Schola Saxonum which would have accommodated Alfred's party and other Anglo-Saxon pilgrims. The Schola Saxonum was established by an earlier Wessex king, Ine, and was large enough to contribute to the defense of the city.
Source: The White Horse King by Benjamin Merkle, pages 17-19
Nyt wyf i gwedy darllen lawr o Urut y Tywysogion etwa, a mi a debygwn eu wybot am y gilid. Pa fford uu petheu y rwng y teyrnassoed? A wydost ti py beth yssyd gwedy ysgriuennu yn Brenhined y Saesson? Atuyd y mae mwy am Alfred yndi.
Have you looked in Brenhinedd Y Saeson? There might be more about Alfred in there. I don't have a copy on me right now, but I can check tomorrow. I doubt it will answer your question, but I always find it interesting to see what the chroniclers think is worth mentioning and what they leave out that's in other texts.
Your question also has me wondering about some other things. To what extent would the courts in British kingdoms have known about the goings-on of other courts? Did they keep up with each other's circuits?