No. Without the bravery/armor training class features access, it will not do anything. If it had language similar to Monk's Robes (which states that you have the described abilities of a 5th level Monk), then it would be a different story. In fact, even if you were a level 1 fighter and had the Sash, it would not work because you do not have the class feature yet. At level 2, you get Bravery so it'll count as level 6, but it will not give you Armor Training early. At level 3, you'll count as level 7 for determining the power of both abilities (and full speed in full plate is pretty awesome).
Likewise, even if you are a fighter but has an archetype that removes one or both of those class features, you would not gain the missing class feature(s) as a 4th level fighter, either.