Again, the answer to your question is YES, you should include your control variables in the model, then run the regression as well as the Hausman test.
The Hausman test is used to decide whether fixed or random effects model would be more appropriate. The null hypothesis in the Hausman Test is that both these types of estimation models are suitable and yield similar coefficients. If they are similar, then it is appropriate to use a random effects model since it provides more efficient estimates. The alternative hypothesis is that the random effects model is inconsistent but the fixed effects model is unaffected, so the two sets of coefficients obtained are different.
For running the Hausman test, you should use the complete model including the control variables.
It is VERY important that you include control variables, and you have to pay particular attention to the fact that the a Hausman test yields different results DEPENDING on the control variables that you account for. Always keep in mind that what this test really does is detecting systematic differences in coefficients obtained from i) a model with individual effects treated as parameters and ii) a model treating individual effects as error components. This difference is very sensible to the control variables.
So, actually, if the null of a Hausman test is not rejected, you should interpret it as statistical evidence of no correlation between the included control variables and the individual effects (thus you are allowed to treat them as random components). Otherwise, there is at least one control variable for which zero correlation with the individual effects is not a statically tenable hypothesis.
Try to take a look at the chapter devoted to Panel Data in W. Greene's classical Econometric Analysis.