Consider a viscous fluid, flowing linearly (say, with velocity $\vec u = [1,0]$ everywhere). Then an obstacle is put in the flow. Would a highly viscous fluid start deflecting around the obstacle earlier (more up-stream) than one with low viscosity?
Your intuition is effectively correct. Basic corroboration can be found in the book Viscous fluid flow, second edition by Frank M. White. In section 3-9.2 he exams low Mach and Reynolds number flow, known as Stokes flow, over a sphere. Surprisingly, the analytic solution for the problem turns out to be independent of the fluid's viscosity. He then draws some comparison to the high Reynolds number, potential flow, solution to flow over a sphere:
This statement essentially provides verification that as Reynolds number decreases, or viscosity increases, that it can be expected that streamlines are displaced further from an obstacle.