Depends what part of "Catholic Europe" you have in mind. The Polish-Lithuanian state, in which Latin Catholicism was the de-facto state confession, openly acknowledged and recognized Eastern Christian communities (Orthodox and Armenian) which became a part of the confessional landscape following Kazimierz III's eastward expansion drive in the 1340s. As a rough estimate, the percentage of Christians in the Polish-Lithuanian state who acknowledged the Patriarch of Constantinople as their spiritual head, hovered at around 40%. This number included not only peasants, but also gentry and powerful magnates.

Perhaps the most well-known Orthodox refugee of the sixteenth century was Andrei Kurbsky, who unsuccessfully led Muscovite armies against Poland-Lithuanian forces during the Livionian Wars (1558-1570). Fearing for his life, he defected and was granted asylum by then-king Zygmunt II August. Toward the end of his life, Kurbsky devoted himself producing translations of the Greek Church Fathers, and as such, was allowed to maintain his confessional identity unhindered.

That said, starting in the sixteenth century, several factors aided conversion among the noble elites. A nobleman was much more likely to benefit from royal largesse of titles, offices and land gifts if he happened to be Catholic. Additionally, as a renaissance-style humanistic education became more in demand, Jesuit-run colleges held a near-monopoly on this type of learning. Sons of Orthodox nobility graduating from these schools were much more prone to conversion to Catholicism. Starting in the second half of the sixteenth century, the Orthodox communities also became vulnerable to the tide of the Protestant Reformation, which scored major conversion successes among the high nobility. Concerned by this trend, Orthodox and Catholic bishops eventually agreed to a regional confessional union, which witnessed the creation of an Eastern Christian Catholic church, that maintained its own separate traditions (including married clergy), its own separate episcopate, while recognizing the papacy as its ecclesiastical head.

TLDR; The late medieval / Early Modern Polish-Lithuanian state had a large native Eastern Christian population, along with various refugees who had arrived there from the east. Although coercive mechanisms of conversion were not implemented, the state offered clear advantages to any nobleman who became Catholic. Peasants were almost entirely exempt from any such benefits. Although not a "conversion" per-se, the 1596 Union of Brest brought the Orthodox community in Poland-Lithuania into a confessional union with Rome, while allowing the former to maintain their cultural and administrative structures.

Borys Gudziak, Crisis and Reform: The Kyivan Metropolitanate, the Patriarchate of Constantinople, and the Genesis of the Union of Brest (Cambridge, MA: Harvard University Press, 2001)

Oskar Halecki, From Florence to Brest (1439-1596), (Chicago: University of Chicago Press, 1968)

I can talk a bit about the existence of Greek emigres in the England during the 15th century.

Chroniclers report that that there were some Greek merchants resident in London at the turn of the 15th century, as the Byzantine Emperor, Manuel II Palaeologus (1391-1425), conversed with these individuals upon his visit to the city, asking for news on Constantinople. The Crowland Chronicle also reports that Greek merchants traded alongside resident Italians in London in this period. A Greek merchant appears by name in the Port of London Ledgers for 1445/6, one 'Georgo de Constantinopolo', an individual who was importing barrels of sweet wine from the Eastern Mediterranean. It has to be said, however, that there was not a large Greek trading community in London, unlike the Italians or Germans, and reports of their existence are fleeting.

The Alien Subsidies Lists, a record of all registered foreign denizens in London, shows two brothers with the last name 'Grekys'. These brothers, who are recorded as the 'Effomato' brothers in later lists, practiced an eastern-based craft of goldwire drawing, creating images from goldwire. The exclusivity of their craft - there were no English goldwire drawers until the 17th century - meant that they could become prosperous, despite being so far from home.

There is also evidence of Greek physicians practicising in England at this time. Scottish King, James III (1460-1488), employed a Greek doctor, Serapion, as did the Italian-born Countess of Kent. The Countess employed one Demetrius de Cerno, a Greek physican who was known have had an English wife and children. The above question concerns the treatment of Greek emigres in Catholic countries and for de Cerno to have married in England shows a degree of assimilation.

Concerning worship of Greek Orthodox liturgy in Catholic states, the response seems varied. Venice, Byzantium's closest Western contact, banned its worship until 1498. There appears to have been no such ban in England, and the chronicler Adam of Usk reports that Emperor Manuel II, along with his soldiers and priests, proudly celebrated the Greek liturgy in the presence of the English king at Christmas in 1400.