It is possible. One of my children never got a fever with strep. Would just feel tired and throat hurt. When you looked at throat you could see white blotches and then we knew for sure.
It's also possible to develop patches on the back of the throat from a virus. Looking in my kids' mouths was the first thing I did when they got a sore throat. If I saw patches, I took them in. A couple times it turned out to be a virus that ran its course. Huh, what a nasty trick.
Don't forget some white patches can be thrush.