It always helps to fix any problems with your license prior to dealing with the prosecutor or court. Prosecutors vary is how much it helps, but generally, a DWLS 3rd charge is a low priority and the prosecutor is more concerned with fixing the problem than with seeking sanctions. The part that is unclear is how it will effect your probation. Your attorney may be able to negotiate a favorable resolution.
If you have violated the terms of your suspended sentence the judge can impose any or all of the suspended jail time as a sanction. No violations of criminal law and no driving without a license and insurance are typical conditions of a Reckless Driving. The court would have to find that a violation occurred by a "preponderance of the evidence." A conviction for DWLS 3 is not necessary to find a violation and the court can use police reports and testimony as evidence against you. Thus, it may not help to be re-licensed prior to court. On the other hand, it definitely won't hurt you (and you need a license anyway).
The answer provided is for educational purposes only. It does not constitute legal advice or create an attorney-client relationship. You should consult an attorney for legal advice regarding the facts of your specific case and designed to help you with your personal needs.
Yes, it absolutely will help. You will also likely have a probation violation on the Reckless Driving.
First, you can expect to receive notice of a hearing from the court where you got the Reckless Driving for a probation violation. This is because you were most likely ordered to have no criminal law violations, and not to drive without a valid license and insurance. As to the criminal law violation allegation, if you can get the new DWLS charge reduced to an infraction, you may be able to avoid being punished for that violation. As to the driving without a valid license and insurance, some court see have held that this means you have to have been driving without BOTH a valid license AND insurance. Thus, if you had insurance at the time, or if the prosecution cannot prove you did not, then you may prevail on this as well.
Second, on the DWLS 3 charge itself, many jurisdictions will readily reduce it to an infraction of No Valid License on Person with ID. However, to qualify for a reduction you must get your license reinstated. Probably what happened is that you had a 3o day suspension on the Reckless, thought you were good to go after the 30 days, but never reinstated after the 30 days, which is a requirement. So it may be a matter of just applying for reinstatement, paying the fee for that, and getting your license before your next court hearing on the DWLS 3.
Third, you need qualified legal representation. There could be a single fact that you left out of your question that could send this entire answer in an entirely different direction.
This answer is my personal opinion, offered for informational purposes only. It is not a legal opinion, nor is it legal advice, nor does it create an attorney-client relationship with anyone reading it.