After unlocking the secret mission, do I need to finish Media Blitz to be able to access it?

Spoilers below.

I have destroyed the appropriate building in the Media Blitz campaign to unlock the secret mission. I got the notification that it has been unlocked, etc. I really didn't want to bother with finishing Media Blitz again, so I aborted.I looked for the mission once I was back on the ship, but am unable to find the mission. I was hoping that the secret mission unlock would work just like achievements, in that you can do what you need to do for the achievement, and abort the mission and still get it. Do I need to finish Media Blitz to be able to access the secret mission?

summary: Once I have unlocked the secret mission, do I need to finish Media Blitz to be able to access it, or can I abort the mission?

Your own experience confirms that yes, you do need to finish 'Media Blitz'.

The secret mission will appear on the star map, same as other "normal" missions.

Edit: note that you will have to play the secret mission before going to Char as once you start that, you won't be able to go back to do it.

Actually, what is happening here is that you cannot unlock the secret mission if you did not unlock it on your first playthrough (which I'm inferring from "don't want to beat again").

If you play through Media Blitz, and do not collect the secret documents, you can't unlock the secret mission. If you then later replay the level after finishing the campaign, and collect the secret documents, piercing the shroud will not unlock.

It is also necessary to actually finish Media Blitz within the campaign as well -- you don't get research points by completing objectives and then aborting (you have to finish the level for the research to accrue) and the secret documents behave in a similar way.