Unfortunately, through tuning files, I was unable to find any answers, so I had to resort to in-game testing.
So, after looking up the definition of \"second cousin\" (English isn't my first language), I created a test family and tried to replicate the definition. So I made a sim named \"a\", her father, her grandfather, her grandfather's sister, her grandfather's sister's daughter, and her grandfather's sister's daughter's son aka the second cousin (jeez that took long to write out).
The results:
I could set a's relationship with her second cousin as spouse in CAS. This however removed a's family ties, so I went and tried to get them married through gameplay.
They could romance each other. They could get married to each other (thank the Lovebug's early proposal for bypassing the 6 hours after first kiss rule!)
They could try for baby.
So yeah: final answer: yes, sims can have babies with their second cousin. Grandparent's (and greater's) siblings won't be considered as part of the family anymore, thus the game allows it.
Proof: The family tree:
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