I just read several sources of FO: NV info but can't seem to find an answer. I'm wondering if it is possible to
I'd like to keep the companion in question on my team while completing the rest.

Pretty sure Veronica's quest is completely independent of Still in the Dark. I believe that I have completed it without doing Still in the Dark.

EDIT: Still in the Dark starts when you enter the BoS bunker.

You totally can do this. By default, Still In The Dark starts when you first meet Ramos at the entrance, but there is no time limit on it, and it is completely independant of I Could Make You Care. Because both quests share the same locations and NPC's, if you first go into the bunker with Veronica it seems like they are related but they are not, I guess you could say they are coincidental.