The issue is that you are still in unlawful status, so it won't hurt and probably won't help. Depending on how long you have been here, you may be eligible for cancellation of removal.
If you are currently in immigration court proceedings there may be a way to get you a work permit in just a few months, that is, if you are eligible as the other attorney mentioned for cancellation of removal or maybe other forms of relief. To be eligible for cancellation of removal you must have been present in the U.S. for 10 years, have qualifying relatives i.e. Legal Permanent Resident or U.S. Citizens spouse/child[ren]/parent[s] and have good moral character. If you'd like to further discuss your eligibility for relief before the immigration court and eligibility for work authorization, please contact me for a free consultation.
Since you were arrested by ICE and already have a court date, you really should hire an experienced immigration attorney who can give you sound legal advise and options in order to mitigate your case. You already have a court date, therefore you need to hire an attorney now. Do not wait.
If you have been in the United States for over 10 years and have a qualifying relationship to a US citizen, there may be a procedure which could help you obtain a work permission and potentially help prevent your removal. That would largely depend on your own individual circumstances though, and any attorney worth their salt would want to have a thorough consultation with you prior to advising you further as to any potential defense or consequences of working without authorization. Since you have court coming up, I would suggest contacting an immigration attorney as soon as you can.