detection - How does the energy of non-resolved spectral lines get distributed in an FFT?

For example, if my FFT has a poor resolution of 170Hz (data sequence length is small due to latency constraints) and I am trying to detect a sinusoid in the 150-250 Hz range, will this FFT be good enough?

I feel if the sinusoid is in the neighborhood of 170 Hz (150-200Hz), my frequency bin at 170Hz will show an increase in magnitude which I can use to detect. But what if a sinusoid is present at 250 Hz? Will its energy be distributed between the 170 Hz bin and the 340 Hz bin? And if so, in what proportion? (perhaps I can use a weighted sum to detect in that case)