There's nothing in the rules that explicitly calls out if a Doppelganger can also copy a Salvaged Omega tech item, so it's a judgement call. You've got options.
Hard Line: Consider any salvaged Omega Tech item to still be an Omega Tech item, simply because duplicating powerful items could turn encounters into cakewalks. I think that's the rationale behind preventing copying Omega Tech items in the first place. You will need to keep a separate, non-Omega Tech version of the character for the copy's stats, which will add an extra bit of bookkeeping.
Hard Line With Exceptions: Allow some items to be duplicated if the player can make a compelling case. I would make the call depending on the item, how it's used, and what it can do. If we're talking about something like a salvaged Fizz Neurojack that attaches to the character's neck and gives a +2 on Athletic rolls, I'd let that slide since you could consider it integral to the character's body, plus the bonus won't significantly impact play. Copying a salvaged Force Axe doing 3d8 force damage and pushing targets 1 square would give me pause.
Allow As Part Of Your Story: You could play with the rules a bit here if you wanted to. Make a power that allows the Doppelganger to copy one salvaged item, then let the character draw it as an Alpha Mutation. Or let the character work on it and eventually make it a permanent power, similar to a D&D Feat. Or have different powers for copying skill boosters, armor, and weapons that need to be learned sequentially.
Permissive: If you're OK with having copies of powerful items in a single encounter, then go for it and have fun. Before you do, consider the ramifications. What if the copy has a powerful weapon that he then hands off to another character to use? That little trick could make some encounters far too easy, especially if the monsters have a vulnerability to something that can be copied.
Your options are open, so go with the one that best fits your game.