Is viscosity proportional to the number of hydroxyl groups?
It is a reasonable rule of thumb, but certainly not always true. 

Compare for example the viscosities of Dodecane ($\ce{C12H26}$, $\mu=1.374 \ce{\; mPa\cdot s}$, no $\ce{OH}$ groups) and Ethanol ($\ce{C2H5OH}$, $\mu=1.095 \ce{\; mPa\cdot s}$, 1 $\ce{OH}$ group) (source). There you can see that ethanol has a higher number of $\ce{OH}$-groups, but a lower viscosity.

That said, I do think you are on to something regarding the strenght of intermolecular interactions, it is just not purely the number of $\ce{OH}$-groups that matters for that. The length of the carbon chain for example (like in the example I mention above) also plays a role.