What if I entered the U.S. illegally or overstayed my visa -- can I still apply for TPS?
Yes. While TPS approval is not a grant of amnesty (or forgiveness) for prior immigration offenses, you can still apply for and receive the benefits of TPS (including a work permit) if you entered or remained in the U.S. illegally.
Yet another compelling reason to apply for TPS is that once you are approved, your period of unlawful presence in the U.S. will be “tolled” or stopped. That means that the time spent in the United States while a TPS beneficiary will be considered lawful for the purposes of adjusting status and avoiding inadmissibility problems. (For further information, see “Consequences of Unlawful Presence in the U.S. -- Three- and Ten-Year Time Bars.”)
source-http://www.nolo.com/legal-encyclopedia/frequently-asked-questions-about-temporary-protected-status-tps.html