The book is from the Saxon Stories series by Cornwell, by the way.
Edit: Just to clarify, he said that after being betrayed by Guthrum and while hiding in the marshes around Athelney.
There was indeed such a community. Anglo-Saxon Christianity was often very fervent, and pilgrimage to Rome remained a common phenomenon throughout the Anglo-Saxon period. Alfred himself had visited Rome as a child with his father, and been personally introduced to the Pope.
Fostering close relations with the Papacy was an important part of the Romanitas central to Anglo-Saxon, and indeed wider Early Medieval political life. Later in the tenth century, for example, King Eadred sent vast chests of silver coinage in tribute to the Pope, which now provide an excellent artefactual reference point for numismatic study of the period. The scale of pilgrim traffic and the devoutness of the Anglo-Saxons meant that there was indeed an 'English Quarter' in Rome, and Alfred founded a hospital there, alongside sending regular tribute and corresponding regularly with the Pope.
Cornwell's idea probably comes from Alfred's contemporary and ally Burgred, King of Mercia. Following his defeat at the Battle of Repton in 873, Burgred goes into exile and moves to the English Quarter in Rome where he lives out the rest of his life with his wife. We have no way of knowing if Alfred ever contemplated a similar move but frankly, it's probably unlikely given what else we know about him.
The whole situation around the 'fall' and redemption of Wessex and Mercia is very murky. The Anglo-Saxon Chronicle would have us believe that Mercia rolled over and gave up following the defeat at Repton, and calls Burgred's successor Ceolwulf II a Viking pawn, but this is largely Wessex propaganda. What seems to have occurred instead is some form of proto-Danelaw, whereby the Mercians ceded some territory, but the Vikings were unable to actually capture the entire kingdom. We know from numismatic evidence that Alfred and Ceolwulf actually seem to have formed a close alliance, and from the Annales Cambriae that Ceolwulf campaigned particularly aggressively along the Welsh border in the late 870s, reducing a number of Welsh kingdoms to Mercian overlordship.
The story of Alfred at Athelney and at Eddington is a fantastic piece of Cerdicing propaganda, a tale of stoic resolve, bravery and snatching victory from defeat, but it actually illustrates the effectiveness of the West Saxon distributed defensive network. At the same time as Alfred is supposedly hiding in the marshes and, according to Cornwell contemplating exile, the fyrd in Devon defeated a second Viking invasion, killing one of the leaders of the Great Army and over 800 of his men, and capturing the 'Raven' banner. This alone implies that a significantly large corner of Wessex was still holding out against the Viking invasion. That the fyrds of Somerset, Wiltshire and Hampshire are able to rally to Alfred at Athelney also implies that these counties are similarly unoccupied and free to mobilise their garrisons. With Mercia also likely actually holding out to the North, Alfred would actually have had a vast array of immediate military options to consider before he thought of flight to Rome.
But of course, snatching victory from the jaws of defeat with a small band of courageous followers is a far more romantic and inspiring national narrative than a likely minor and short-term territorial setback in a period of highly mobile seasonal warfare.