Non-resonant RLC band-pass filter
My question is: is it possible to find L and C values to create a
  band-pass filter without resonance.


There is no such thing - even if the circuit is so over damped to be daft, there is still the natural resonant frequency of the circuit which is \$\dfrac{1}{2\pi\sqrt{LC}}\$.


  Is this circuit a real band-pass filter, or just some look-a-like?


Yes it absolutely is.


  And is my statement that this circuit is not in resonance correct?


No it isn't.