That'd be conjecture. The Gallic 'druids' were trained differently. While they had similar practices (mnemonics, constant memorization of lengthy names/places/family trees), this stems from an earlier tradition that branched into the Gallic and British religious practices.
However, when 'deals' were made that would affect the religious lives of the Gauls and Britons, they would no doubt meet to discuss such matters, and they both used 'druids' (Gauls didn't really have druids, in the technical sense, though they had a near identical class) as diplomats. Gallic holymen going to Mona wouldn't be going there for training, they'd be going their to discuss matters affecting the British tribes, and the Gallic kingdoms, and what their organizations roles would be in these events. However, their were too many of these men to say they were all sent to Britain, they were trained by the elder Carnutes, thus, trained at home, in Gaul.
British Druidae had different practices than Gallic Carnutes. They used different sacred objects, they held different positions in society, etc. If Gallic 'druids' were trained in Britain, British gods and practices would be more prominent in Iron Age Gaul. Aside from some 'border gods', Gauls and Britons worshipped very different gods. These gods required special practices, such as specialized ritual executions, animal sacrifices, vegetable sacrifices, elaborate chants, songs, and poems, etc. It would make no sense to send a holyman to learn how to worship gods that are not worshipped in your kingdom, and then bring him back, expecting his practices to sync up with those practices done in your own lands.
Aside from worship differences, and mnemonics being taught by elders, there is the combat role of religious leaders in Gaul, versus that in Britain. In Gaul, Carnute Cingetos engaged in war, organized into units, and assisted Gallic armies in fighting invaders. They were VERY skilled, implying years and years of training. But British druids did not fight, except in very rare cases. Those years of training had to be done in Gaul. Aside from practical fighting skills, they would need to learn how to fight using Gallic tactics, not British tactics, because combat in Britain is different than combat in Gaul. It makes no sense to send these men to learn how to fight like tribesmen, when you need them to fight like professional soldiers.
The point is, Druidae were very different than their 'equivalents' in Gaul and Hibernia, which would be most likely to deal with them. Both Gaul and Hibernia had their own religious leaders, they didn't NEED Druidae. Their own practices and gods and the state of warfare they engaged in required them to be trained differently. Maybe a few were 'cross-trained', sent to eachothers religious and scholarship centers to learn how they do things, but that's not giving dominance to Mona. That's like modern Catholic and Buddhist monks engaging in 'religious exchange' programs, where they visit eachother's monastaries, and observe techniques of meditation, prayer, and devotion. They don't adopt those practices, necessarily, but they may integrate what is conducive to their own practices, and gain knowledge of additional possible techniques. This would allow these clerical members to gain increased knowledge of the world around them, and refine their religious and philosophical techniques. That doesn't equate to training though, since, as mentioned, training in that manner wouldn't really help them be more effective religious leaders in their own lands.
Modern revisionist, despite any proof to it, often put more stock in the British druids than there really was. The Celtic world did not revolve around them, but for whatever reason, some people like to think it did. They were no doubt powerful in Britain, but they didn't control the religious life of the Gauls and the like. The Gauls, actually, seem to have had a bit more effect on the Britons, religiously. Religious figurines, not to mention gods, were taken from Gaul, to Britain, first by traders (the figurines), and then the Romans (Gallic gods). British gods were worshipped, sometimes, in the north of Gaul. But if the British druids had really had any profound hold on Celtic religious life outside of Britain, British gods and practices would've been a bit more prominent.
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