Couple of points
1.) Adamjt13, the comp pick guru, wrote this
"In order to qualify for the comp equation, a player must have been a true Unrestricted Free Agent whose contract had expired or was voided after the previous season (i.e., he cannot have been released by his old team); he must sign during the UFA signing period (which ended July 27 last year); if he signs after June 1, he must have been tendered a June 1 qualifying offer by his old team; his compensatory value or contract value must be above a specific minimum amount; and he cannot have been permanently released by his new team before a certain point in the season (which seems to be after Week 10) or, possibly, before getting a certain amount of playing time, unless he was claimed off waivers by another team." Emphasis added by me.
I take the above as if Blount is claimed that he will not count in the comp pick calculation for the Patriots
2.) the claiming order is by standings.
3.) New rule/process this year - We will not find out if the Patriots put in a waiver claim