Can all of the Steam keys at gamehag "unlock" restricted accounts?

As all of the Steam users know, Valve has implemented the system of restricted Steam-accounts a few years ago in order to combat trolls and other unserious users.

Personally I think this affects serious Steam-users who only start their accounts to play their favourite f2p-games and/or other games earned through giveaways, since they can't communicate with their close friends. I mean, not everyone is interested to play with total strangers.

Recently I've managed to convince a friend to start a Steam-account and of course it's restricted. She is only interested in playing the f2p-games (like Team Fortress, Mobius Final Fantasy, Champions Online and Sven Co-op) so she definitely isn't interested to spend $5 USD to unlock her account. My goal at gamehag is to unlock her account, and I plan it to be a surprise for her.

So my question for the community is the following: Can all of the Steam keys at gamehag "unlock" restricted accounts, or are they considered "gifts or games bought at a retailer" according to Steam Support?

Because if gamehag's Steam games can't unlock her account, then I'll just have to aim for the Steam Wallet instead.

@Clound12 That's what I suspected. Thanks!

You need to get at least 5$ to the account but after 30 days you will lose all the money, so consider buying staff in the market so you can sell it. (It works I think but I haven‘t tried it yet.)