Can the GoG version of SSTSE be activated on steam?

No. This is not Serious Sam: The Second Encounter HD, it is the original Serious Sam: The Second Encounter.
Also, GOG games are DRM free and will use generic GOG keys (where applicable) as part of the install (unique keys can be asked for if required for multiplayer).
You can always add it as a Non-Steam game though, but then that's really just adding a shortcut to it in your Steam client.

full price comparison:

Serious Sam HD: First Encounter: $15
Serious Sam HD: Second Encounter: $20
Gold edition = 2 HDs + 2 Orig: $40

Essentially, for $5 extra, they are giving the previous orig versions of both. On GOG.com these are $20 in total.

On principle, I would have agreed to pay $10 for SS orig even if the steam version is $5 (with the HD purchase). But $20 vs. $5 for the same 2 games...

It depends on how you want to have the games. If you get them via Steam then you get them with Steam DRM. Get them from GOG and once downloaded they are yours, DRM free, no login needed.