First of all, many of the folks that try to help folks in here also post in Reddit and Federal Soup.
To answer the question I think you are asking up front - NBIB (OPM) does not determine if you are medically qualified to be in the military. The military does that examination. If NBIB find that you lied about mental health, drugs, or alcohol treatment, yes, we report that to the military.
To answer the hidden question - NBIB does not have access to your MEPS medical records, though the military does have access. The military does provide access to your military record, which includes MEPS processing, enlistment declarations, etc.
NBIB is not trying to “get you”. Agencies are not trying to hide information or issues from NBIB. The background investigation is to help determine if you are trustworthy, reliable, and responsible enough for government/military employment (this includes contractors) and to hold a position of trust (security clearance/public trust) .
This is not a process to game. This is the big time - lying, trying to lie, hiding can get you in jail (at worst), dismissed for fraudulent enlistment, barred from government employment, or simply released (at best). Report what the questionnaire ask you to report, using the start date you sign the form. Read the questions literally and answer literally. If additional concerns are developed, the Agency will ask us to talk to you about it — you don’t want that additional concern to be something that you were required to report but did not.