yes it can and it varies by person. My ex and I had to stay with his grandma for a short time, she is terrified of snakes and did not want them anywhere near her house but I had no choice. I explained how they were locked up to try to calm her. I carried the tubs in covered with towels and she had a complete utter shock and fear on her face and was frozen, could not move, even though she could not see them. I kept them in a spare room which I installed a lock on as well to try to relax her but she was uneasy the entire time they were in the house and had trouble sleeping. I thought she had exaggerated her fear and it wouldn't be a big deal but oh boy... It was horrible and I felt terrible about it, luckily it was only for one month.
My friend has a fear of spiders. She works to try to overcome it by forcing herself to look at photos of them, even seeing pictures she tenses up and gets uncomfortable. When she's go to reptile shows and shops with me, I'd have to point out there area where the spiders were kept so she could avoid it.
It's a very real and sometimes crippling fear for some people that can be incredibly difficult to overcome.