No. “Player marriage” as a mechanic:
Encourages meta-friending.
Is tonally removed from the rest of the game.
Is shallow: It ties into no other game systems and only concerns the two people who are being wed, and the chaplain.
Contrast marriage with, for example, radiation, which concerns engineering, medical, and regular Joes wandering maint while the SM explodes. Or bananas: Clowns who want bananas can grow them, but Botany exists. So if Clown wants bananas, funny boy is encouraged to ask Botany to grow them, which I claim is good because it makes the station more interconnected and alive.
Two random Civillians getting married discourages interesting cross-station interactions, and instead encourages metafriend navelgazing.
I appreciate the sentiment of wanting to add more role-play opportunities into the game. I wish Paradise was less LRP and NoRP. But I don't want player marriages.
So, NanoTrasen, banal corporate evil that it is, allows its employees to marry one another! But to one and only one other person. Why are we emulating weird marriage bureaucracy in funny spess game? What have you got against polyamory?