You have been charged with DWI, not DUI. DUI is for people under 21.
If your attorney told you to include the information, then include it in a draft letter then share the letter & your concerns with your lawyer. It is a legimate concern if you attended multiple centers, especially before your arrest. In my opinion, that would indicate that you have a severe problem that even treatment has not been able to fix, and if I were a prosecutor I would guess that you have been DWI many times before but not been caught.
No, they do not have the time & resources to search and furthermore, they could not discover the information if they did because it is protected medical information releaseable only with your permission.
Although I have answered the question to try to help you, you should consult with a lawyer in your area in person on the matter. In addition, my answer does not establish an attorney-client relationship between us.
Pre-trial interventions are geared toward offenders who made a one-time mistake and have no criminal history; and, is a privilege not availed to most people charged. Thus, to be approved for this privilege you will likely be required to provide information you would not legally be required to provide otherwise due to 5th amendment violations.
If the prosecutors in Austin require disclosure of prior treatment to be approved for the pretrial intervention, then you must be honest and disclose it. Be careful, if you disclose this data under a pretrial intervention application, and the application is NOT approved, the prosecutors now have this admission from you. Ask your attorney about including a confidentiality non-disclosure provision in your application if possible.
There is no requirement to shaire any informaiton with most courts. It can be either a positive or negative to your situation. You will need to consult with an experienced attorney who can review all aspects of your case and help you determine how disclosure of this information will apply to your case.
While the court cannot compel you to offer testimony against your interests, the state can possibly discover this information if they dig deep enough. Additionally, if you attempt to resolve your matter through a pre-trial program there will likely be a alcohol evaluation. If you answer the questions honestly, which is truly in your best interests, the extent of your problem will possibly come out.
Bottom line, discuss all facts and your concern with your attorney and allow him/her to advise you about what the law requires adn mandates.