I've been playing Everquest 2 recently and running "solo" with a Mercenary companion (what some call "molo").... my swashbuckler can become invisible to the point I can bump up against foes in the face and they won't see me. It's a fantasy setting, so even though it's supposed to be rogue stealth,not "invisibility" I sort of roll with it.
Thing is, my companion ~doesn't~ become invisible. She just stands there, seven feet of plate-armored beauty, casually looking around as I creep amongst our foes. Sometimes the foes will even turn to look at my Companion as if to say, "Hey, there. Good thing you're not a thief who's not supposed to be here".... of course the minute I turn stealth OFF (and/or attaack) the foes will realize, "Oh, hey, you're not supposed to be here!" and attack my companion (and me).
And if there are foes that CAN see through my "sneak", and yet I am far enough away from them that they won't be alerted, and yet my ~companion~ is within their line of sight then they will aggro on us both.
In Star Wars: The Old Republic, my Smuggler had a stealth field generator which made me invisible ~and~ it made my companion invisible, too.
Since Stealth in Fallout is, I believe, supposed to be more "skillful hiding/moving" than ~magical~ invisibility (Chinese Stealth Suits excluded), it will be hard to avoid detection, I would think. And having a companion out? Looks like that would only make things worse. Especially if the Companion is clanking around in power armor or smells like a wet dog, etc.
I don't recall seeing anything about Lone Wanderer perk affecting your stealth success, although that may be because (a) having no companion inherently makes you harder to spot so no need to mention it explicitly, OR (
having a companion has ~no effect~ on your personal sneaking ability in which case having one or not is irrelevant.