I think it depends on the camera. I had one of the ealier Deer Cam models, and it had a noisy auto focus, a " red eye" light and noisy film advance. I would say it was spooking about 25% of the deer in the photographs. Here are some examples taken over a scrape:
Today' s cameras are much quieter and I do not think they spook as many deer. However, because I was having so many problems with that first Deer Cam, I ending up switching to a digital camera now with an infrared flash. Picture quality is sacrificed for stealth, but I have not had any deer react to the camera at all and I can take/store more pictures this way.
I would not recomend that everyone switch to an infrared flash, but I think they can be effective.