I'm sure they've thought of the NA players and will schedule all events to suit everyone as best as possible. The only issue could be champion dominion which is generally a fixed time for all on Wed and Sun. Those fights may be later for the EU base to accommodate the NA base a bit more. But until we see the game, who knows?
As regards how busy the EU base is over night. It definitely isn't as busy as daytime EU, but you'll still have a decent amount of people on. With the NA and EU merging, the server should have a good population from around 3pmGMT till 8amGMT the next day.
Cheers!