While I pondered a little earlier today if Justin Blackmon would be subject to potential league discipline earlier and outlined some of the new CBA where it would apply, it does look like the air has been cleared and we have an answer. According to NFL spokesman Greg Aiello, Blackmon is subject to the NFL's drug and personal-conduct policies. This is not necessarily mean the Blackmon will be suspended, however.
It all depends on how the league views the offense. If the NFL views it as a first-time offender offense, given Blackmon's previous DUI occurred in 2010 when he was an NCAA player, he could just be placed in the league's program and receive possible treatment plan and random testing. This would likely result in just a fine from the league, if that.
If the league views it as a multiple offense type of deal, he could face a possible suspension. While Blackmon's first offense occurred while he was still an NCAA player at Oklahoma State, the NFL has set precident before punishing players for their transgressions before entering the NFL. Last season, the NFL suspended Oakland Raiders quarterback Terrelle Pryor five games for "decisions that undermine the integrity of the eligibility rules for the NFL Draft." Basically for entering the NFL's supplemental draft to avoid a suspension and likely being kicked off the team at Ohio State.
I don't think Blackmon will receive anything other than a fine in this case, but we'll have to wait and see.