Yeah, I am also wondering if Finch actually wants the machine to survive the virus.
According to the Decima guy, it was Finch who leaked the source code on the laptop in Ordos. Perhaps it was his intention all along to have someone help him destroy the machine or maybe Decima is even one of his many companies. By giving Reese the full administrative access (which Reese will of course pass down to Finch since he has no clue what to do with it), Finch could use that access to destroy the machine from the inside out.
With the machine gone, the Northern Lights project would cease to exist and would give Finch the oppurtunity to get back with Grace, maybe that's what he's after?