As a function of frequency, the answer is in the positive. This follows from the so-called fluctuation-dissipation theorem.
Incidentally, in Landau & Lifshitz - Fluid Mechanics (Vol. 6) a relevant discussion can be found under the heading "Second viscosity". Here one finds a description of the physical mechanism whereby viscosity becomes complex.
The following is also a relevant reference:
http://www.sciencedirect.com/science/article/pii/0378437181900327
By considering the "concentration-autocorrelation function" as a functional of frequency, one will directly obtain the imaginary part of the viscosity. This is in fact the framework in which one applies the above-mentioned fluctuation-dissipation theorem.
In linear response theory a response function is generally complex. Depending on how you set things up, the real part may correspond to a conservative response (say, a shear modulus) and the imaginary part then corresponds to a dissipative response (say, a viscosity). Accordingly, an imaginary component in your viscosity is nothing but a conservative response, i.e., it would correspond to an elastic modulus. Having both conservative and non-conservative responses is perfectly possible. Such fluids are called "viscoelastic."
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