An important question since if they do and you are unemployed then you are likely to remain unemployed. This leads to a group of long term unemployed who find it almost impossible to become re-employed. I have discussed this idea before, see for example here and here.
Now addition evidence on the issue comes from a paper in the most recent issue of the American Economic Review (Vol. 104, Issue 3 March 2014). The paper is “Do Employers Use Unemployment as a Sorting Criterion When Hiring? Evidence from a Field Experiment” by Stefan Eriksson and Dan-Olof Rooth. The abstract reads:
The stigma associated with long-term unemployment spells could create large inefficiencies in labor markets. While the existing literature points toward large stigma effects, it has proven difficult to estimate causal relationships. Using data from a field experiment, we find that long-term unemployment spells in the past do not matter for employers’ hiring decisions, suggesting that subsequent work experience eliminate this negative signal. Nor do employers treat contemporary short-term unemployment spells differently, suggesting that they understand that worker/firm matching takes time. However, employers attach a negative value to contemporary unemployment spells lasting at least nine months, providing evidence of stigma effects. (Emphasis added)
So again we see that the longer you are unemployed the less likely you are to become employed.