I highly doubt it.
The issue is that you can't adjust your status unless you have a 245i exemption if you are undocumented. Keep in mind that this is not like marriage where you can be a visa over-stay and adjust your status. Also, even if you were hear legally (ie. an international student), there is a whole set of rules that have to be followed for the employer to prove that they tried finding a citizen.

I almost had a shot at this actually before the cutoff date of the 245i rule but I didn't have a degree yet.