Testfor command for commands blocks doesn't work fine for non-player scores. As we can set scores for non-player, I assume we also can test non-player score as well.

For this test, I simply put a button on a command block, with a comparator out and a redstone lamp

/scoreboard objectives add testObj dummy
/scoreboard players set MyCharacterName testObj 10
/scoreboard players set FakeName testObj 10
/scoreboard objectives setdisplay sidebar testObj
>> OK
/testfor @a[name=MyCharacterName,score_testObj_min=5]
>> OK
/testfor @a[name=FakeName,score_testObj_min=5]
>> NOK