CWOF is not a conviction for the purposes of firearms licensing but, in the case of DUI, is structured to carry penalties that can leave the defendant who is not paying close attention thinking they were convicted since penalties (court fees, alcohol programs, insurance increases, etc, etc.) are at a level that renders such a CWOF as basically a "conviction without the full stigma of a record". A DUI CWOF is treated as if it were a guilty plea for the purposes of registry action; insurance surcharges; and will even be treated as a "prior offense" if the defendant is charged with another DUI at a future point in time.
If you are treated for "habitual drunkenness", yes. If you have a post 1994 MA DUI conviction then you are federal disqualified for life unless you get a governor's pardon with specific restoration of gun rights.
Furthermore, the BATFE does NOT recognize a FLRB (MA Firearms Licensing Review Board) restoration of rights, and will NOT remove a disqualifying conviction from the NICS record check database, or overturn a NICS denial, even if you prove the offense that DQed you is one for which the FLRB has issued a state level rights restoration.
Oh, and on the pardon - the form asks if you are requesting restoration of firearms rights. You will not trick the system by trying to convince them you just want your good name back and hoping that firearms rights come with the package. They will not be restored unless the pardon board/governor explicitly chooses to grant said relief from disability to the applicant.
And while we're on the topic, be sure to report all hotel fires and make sure any bank you are working at is solvent as "failure to report a hotel fire" and "receipt for deposit by insolvent banking institution" are both MA disqualifiers.