The answer, as you guessed, partially depends on the actions of your employer to cooperate with IDOL and also partially depends on the amount of work IDOL has to handle. As you can imagine, when the economy is down employers start to feel financial pressures and sometimes skimp on employee wages and contract benefits. IDOL is currently busier than normal, but Illinois statutes pertaining to IDOL (and other employment agencies, such as the Department of Human Rights) do impose time limits on investigations.
In your case, the relevant rules states that when an employee files a claim under the Illinois Wage Payment and Collection Act within 180 days of the time the wages come due IDOL must provide the employer ten days to respond with an explanation and any evidence. IDOL then typically gives the complainant (you) ten days to reply to the employer's response.
At that point, if IDOL can resolve the dispute then it will. Otherwise, it will schedule an informal hearing before an administrative law judge who will hear oral argument, look at presented evidence, and then render an opinion. This route typically takes many months to complete.
NOTE: This answer is not intended to be legal advice and should not be construed in that way. This answer does not create an attorney-client relationship and no such relationship may be created absent a signed retainer agreement. The author is licensed in Illinois only, and his answer is for educational purposes alone.
If your employer will hinder them, you need to either file your claim yourself in the circuit court, or hire a lawyer. Thant is my opinion based on many experiences with IDOL. Otherwise you may very well end up waiting years to find out the Department has decided your claim has no merit, and then the statue of limitations has run, and you are left with nothing.
When dealing with overtime wages, it is to the Department's descretion as to when, or if, they ever get to your file. What is most important to keep in mind is that there is a three year statute of limitations on overtime claims in Illinois, this means that if you worked overtime for three years, you are losing each weeks overtime compensation to the statute of limitations while waiting for the department to investigate your complaint. The clock of the statute of limitations does not stop ubtil you file your case in court! I have personally seen the Department take well over a year to investigate, then decide not to enforce their findings, and therefore, the claimant no longer had any remedy, as the statute of limitations ran out while waiting for the IDOL.
Also, IDOL does not have any duty to enforce your claim. I have seen them work cases from mediocre to gar beyond incompetent. It is very important to keep the time while the Department in investigating.
Moreover, it is often fairly simple to prove an overtime case. Even if you do not have complete records of pay, the courts recognize that it is an employer's burden to keep complete records. Thus, if you can produce proof of some overtime, the courts will often allow a plaintiff to apply the weeks wherein he can prove he worked overtime pro-rata to the rest of weeks where records are missing.
You either need to find a lawyer, or take the time and research the laws to prosecute the case yourself. Just my opinion