Oh yes it is possible !!
My younger sister did two kidney infections without any pain at urination, six years ago.
The second time she had a kidney infection was in September 2010, at the same time I caught a pericarditis (so we had our fair share of serious illness).
The first time, she had only a 41°C fever (no idea in °F, but it's a very high fever, I remember she was completely unable to do anything besides staying in bed. I don't remember if she was delirious or not with such a fever, but it wouldn't be impossible). My mom thought about a gastro-enteritis, it was instead a pyelonephritis (kidney infection).
The second time, I don't remember if she had fever or not, but she did have kidney pain. It is the main symptom on kidney infections, the others may not show up in the most atypical cases. If she had fever which I am not sure, it was a low grade one, like 38°C.
So, what you say is definitely yes.