As I've said before, I guess once again CL has been shown to be a bit of a myth in being the deciding factor of a transfer. Granted there's the odd exception but for almost every player generally if you pay them they come. The kind of sums being thrown about would have been difficult to turn down for a guy getting his first massive contract. And given their new manager and whatever other spending, Chelsea will be back in the CL next season and won't be far off winning the league. Last season was as much a blip for them as it was for Leicester.
Probably a lot depends on the player - if you're an affirmed player who's been around awhile and have already made a bit of money, the lure of the Champions League (especially if the club has the chance to do well in it) can be an important selling point.
But like you say, if you've just been offered silly money for the first time, you'd be hard pressed to turn that down - and on balance on probabilities, Leicester's episode in the Champions League probably won't take them too far, and you'd expect to end up playing in that competition anyway with Chelsea at a point sooner rather than later.
Leicester could get a horrible draw in the group stage and that's it. I remember a few years back where the champions of England, Spain, Germany and Holland all in the same group because Dortmund and City had a low UEFA coefficient and not a high seed, Leicester likely to be in a similar situation.
Seeding's been changed now, so that the champions of top 7 ranked countries, along with the defending European champions, are all top seeds. So Leicester will be in Pot 1 along with Barcelona, Real Madrid, Bayern, Juventus, and PSG, so that will help them a lot. But they can still get tough opponents, as they could still end up getting the likes of Atletico Madrid, Dortmund, Sevilla, Napoli, and Leverkusen from Pot 2, and depending how the qualifying goes, even Pot 4 could have really tough teams in it - potentially PSV Eindhoven and Sporting Lisbon for example.
EDIT - Buffy beat me to it.