Pro-athletes are deeply competitive beasts. In the one week of Aussie Rules football we had in empty arenas before it got suspended, the first 10 mins of each game were a bit weird for all involved, but the contests quickly got more intense as the competitive juices kicked in and by about a third of the way in the games were looking pretty normal. I wouldn't say they were going at 100%, but at least 90% compared to a game with fans.
Finals are admittedly a different matter. I suspect the gap between a regular playoffs intensity and what happens in an empty arena might be slightly greater. But Stanley Cups and the like are so incredibly hard to win and many good players never even get close to one. I think the competition will get pretty heated and physical quite quickly as players get back into form and it begins to really dawn on them what's at stake. Some teams will respond to the unusual circumstances better than others but thems the breaks and the same can be said to some degree of every playoff series.
So as long as the format that the playoffs are ultimately played in, if ever, is deemed fair for all involved, then I think the eventual winner will be accepted as legitimate and deserving. Firstly because it's going to take a special group to be able to thrive in such strange, compromizing circumstances, and secondly because I'm sure the games will turn out to be very competitive with everyone giving their all in search of the ultimate prize. It's going to be weird and not ideal for everyone, fans and players both, but we'll get a worthy victor.
We'll also get used to it, since sports are almost certainly going to be taking place in empty arenas all over the world for some time before crowds are allowed back in.