Transitivity of Auto-Specialization in GHC

From the docs for GHC 7.6:

[Y]ou often don’t even need the SPECIALIZE pragma in the first place. When compiling a module M, GHC’s optimiser (with -O) automatically considers each top-level overloaded function declared in M, and specialises it for the different types at which it is called in M. The optimiser also considers each imported INLINABLE overloaded function, and specialises it for the different types at which it is called in M.

and

Moreover, given a SPECIALIZE pragma for a function f, GHC will automatically create specialisations for any type-class-overloaded functions called by f, if they are in the same module as the SPECIALIZE pragma, or if they are INLINABLE; and so on, transitively.

So GHC should automatically specialize some/most/all(?) functions marked INLINABLE without a pragma, and if I use an explicit pragma, the specialization is transitive. My question is:
is the auto-specialization transitive?

Specifically, here’s a small example:

Main.hs:

import Data.Vector.Unboxed as U
import Foo

main =
    let y = Bar $ Qux $ U.replicate 11221184 0 :: Foo (Qux Int)
        (Bar (Qux ans)) = iterate (plus y) y !! 100
    in putStr $ show $ foldl1' (*) ans

Foo.hs:

module Foo (Qux(..), Foo(..), plus) where

import Data.Vector.Unboxed as U

newtype Qux r = Qux (Vector r)
-- GHC inlines `plus` if I remove the bangs or the Baz constructor
data Foo t = Bar !t
           | Baz !t

instance (Num r, Unbox r) => Num (Qux r) where
    {-# INLINABLE (+) #-}
    (Qux x) + (Qux y) = Qux $ U.zipWith (+) x y

{-# INLINABLE plus #-}
plus :: (Num t) => (Foo t) -> (Foo t) -> (Foo t)
plus (Bar v1) (Bar v2) = Bar $ v1 + v2

GHC specializes the call to plus, but does not specialize (+) in the Qux Num instance which kills performance.

However, an explicit pragma

{-# SPECIALIZE plus :: Foo (Qux Int) -> Foo (Qux Int) -> Foo (Qux Int) #-}

results in transitive specialization as the docs indicate, so (+) is specialized and the code is 30x faster (both compiled with -O2). Is this expected behavior? Should I only expect (+) to be specialized transitively with an explicit pragma?

UPDATE

The docs for 7.8.2 haven’t changed, and the behavior is the same, so this question is still relevant.