The way I see it is there are two linked but separate issues here:
1) Will UK citizens have the right to work in the EU post-Brexit.
Unfortunately nobody knows how this will play out, current negotiations seem fixed around current expats. If Britain insists on an end to free movement then I would expect the EU to do the same. Pilots may then require visas and 'EZY Europe' would be restricted to hiring mostly EU pilots. Even if visas were easy to obtain then you could imagine a strong preference for EU candidates being put in place.
2) Will EZY base transfers be possible between 'EZY UK' and 'EZY Europe'?
At least in the short term this is unaffected by Brexit and has maybe been talked about internally? At present I understand that moving UK-France/Italy etc is relatively straight-forward (if there's space) but moving UK-Switzerland is rarer and more complex as it's a separate legal company. If the new 'EZY Europe' operates like 'EZY Swiss' then placements in the continental bases for cadets and experienced pilots alike might become less common.
In summary, lots of ifs buts and maybes
I personally can't see how EZY's new European entitity is going to be a positive for their UK pilot recruitment but I hope to be proved wrong.