It will not.
On crates behalf Medierra has stated that the GOG.com redeem code will be placed on the humble bundle site account we have all been visiting (I’m assuming it’s a redeem code not a serial key; probably semantics I know).
It’s a couple of pages back, but for accuracy always go with a primary source.
In my actual experience using Galaxy, it does not do much checking as I have had other people install games on one of my pc’s (I actually have 5 systems & 2 primary gaming; only just tried out linux for the first time a month or two ago to see how gaming was coming along there too)…
Anyways Galaxy saw them as it registers a directory as containing GOG games, it scanned and added those titles to the list of installed ones… even started updating them (successfully).
This is for games I didn’t purchase myself for a galaxy account that I always assumed was linked to my login only.
Obviously it is not; it is seemingly fairly detached from the main site.
I could probably gripe that it doesn’t seem to allow me to ‘hide’ them from the install list, but when I can turn off auto updating & that I don’t find scrolling that much of a chore I kind of don’t worry about it.
By the way those considering Linux as a move away from windows I will say two things…
a) All distro’s seem to still require you to be comfortable using MS-DOS style CMD.exe line input (and I am/was) for getting things working, &
b) GOG games did not take me much to get working, unlike minecraft though that was primarily the hassle java presented wanting specific libraries.
I was not happy with the Linux experience; if it’s making progress to becoming more friendly I shudder to think how it was before I ‘met it’.
As to SLR’s post, I did read & ‘digest’ Dargenus’s ‘Genesis’ 
, the problem I had & I’m not going to engage in trying to tear it apart or providing fodder for it, was that I found it overly aggressive so much so that it strays a little far from the reason he clearly has applied to underpinning the subject matter.
To tell someone what to think and to simply educate them are two different things.
“Not being able to play something you paid for, something that requires no internet access, because a service platform decided you are untrustworthy is pretty jarring and makes one not want to purchase a game on a service platform ever again. “Why the hell did I buy this on Steam?” was going through my mind.” You can feel the rage ebbing from it.
The problem with arguments as opposed to discussion is that it creates a barrier intrinsically and instinctively between those involved and accordingly the goal devolves from the navigation of the issue at hand to harm minimization (risk to self including stress).
He makes grandiose claim that a non-DRM version will not exist, where arguably there can be no certainty one way or the other.
Medierra states they have signed a contract with GOG, I am inclined to believe him.
If I look at my options, if I didn’t believe him there is simple and open recourse (refund); should I demand ‘pics or it didn’t happen’? there are reasons to deny (GOG may want it’s dealings kept under NDA against competitors: reasonable); and lastly should I believe him, but that comes down to what I have to lose or gain when I accept that I am not looking for a refund at the moment.
To not take him at his word while under duress, is little more than to torture him in a form of inquisition for no practical purpose; and I say torture for a reason.
He has been saying what has occurred, but it is not accepted; so then what? Do we pile on more stress till he either has a heart attack, quits altogether (though unlikely) or just says what he thinks we want to hear… then has to repeat the situation when the reality creeps back up on him?
At this point it just seems malicious (though technically that word only means done with intent).
Illiousintahl is right; the spellchecker would mark around 30% of my text in red, not because I just became inapt.
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