Even RAW it doesn't.
Check the wording on Unwieldy itself, it quite specifically applies only to attacks made with the particular weapon that has the Unwieldy rule. Not attacking with an Unwieldy weapon? Then Unwieldy does not apply.
It is possible to twist the reading of the FAQ question as changing this, but that's: A) Not something an FAQ can actually do, being FAQ instead of Errata. B) A gross misinterpretation. C) Really super not fun, and a massive stealth nerf to Melta Bombs as well (Carrying Melta Bombs? Surprise, you're Initiative 1).