I don't know. My friend has a theory, though, that only the companions with scars are LIs, so if you've got a scar, you're shaggable. Her theory's just about as good as any on BSN, really. Not that I believe her, but to play along a bit: the only scarred companions I've seen are Varric, Iron Bull, Cassandra, and Solas. Vivienne appears flaw-free and there's not a good enough close-up of Sera, "Dorian," or Blackbeard to tell whether they've got 'em or not. Cole? Just... no.
In the end, it's just a crazy theory, anyway, but what's BSN without a crazy theory every now and then, no?
As for whether I'd approve of a Varricmance... yes, yes, I would. My eventual dwarf Inquisitor isn't attracted to humans, qunari, or elves, so if Varric is unavailable, she'll probably remain single and just end up in a bromance with the guy. Girls can have bromances, right? Or is it just a guy thing? I'm not caught up on today's lingo to know either way. Were "bromances" even a thing way back in the 80s? 