In my experience: Yes, the passengers notice, at least for some lightning strikes.
I was flying from San Francisco to Chicago, this was sometime in the 90s. There was a big snowstorm coming in to Chicago, and all you could see out the windows was snow illuminated by the landing lights. There was the usual murmur of conversations going on in the cabin, and all of a sudden there was an almighty BANG and the cabin went completely silent - everybody had stopped talking and was probably holding their breath. Several seconds later (seemed like a long time) the captain came on the PA and said
Nothing to worry about folks, we were just hit by lightning. We will be on the ground in Chicago shortly.
I am 100% certain that every single passenger on that flight "noticed".