What is the effect of current noise in this op amp circuit?
Assume V= 0 for now. Since the op-amp is ideal (other than noise), the inputs are always at the same potential (due to the the output voltage changing and through presumed negative feedback). If you have a current I_n then, in order for the inputs to be at the same potential, a current must be flowing through R3 equal to I_n. The resistors R1 + R2 across the inputs do not have any effect since the voltage across them is always zero (if R1 and R2 were both shorts you'd have a 0/0 situation). 

However, the way you have drawn this circuit (floating V) no current can possibly flow through R3 because you don't have a ground anywhere. So no matter how high the output voltage gets, no current flows. With an ideal op-amp and ideal parts this creates another paradox.