Mike Laidlaw says the companions will tease whoever the Inquisitor is dating and pester them for gossip etc. Presumably that same would go for Cullen's romance, especially if ML was being honest about that Cullen-centric, multi-region, expansive quest he tweeted about. If Cullen's there and so are our companions then there's bound to be some banter regarding that topic.
As for how he'd react? I think it depends on what they'd ask him, LOL!
OMG it's true??? I thought our companions were supposed to be grown-ups
lol, it's going to be fun.
Leliana: Sooooo, you and Cullen!
Inquisitor: Me and Cullen what?
Leliana: You know what. You and him, spendings evenings together in the war council room. I know what you two are doing behind the closed doors *wink*
Inquisitor: He's teaching me about military stuff... 
Leliana: Oh, that's how you call it now!
(later)
Leliana: So, Cullen, you have found your true love at last? 
Cullen: What? Where? *looks around*
Leliana: Oh come on, you know who I'm talking about! She's a beautiful and powerful woman...
Cullen: Look, sister Leliana, just because we had the same training, it doesn't mean I'm in love with her.
Leliana: What? But she's a mage...
Cullen: Oh no, now you are going to tease me about Enchanter Vivienne? We've barely talked. Two times. The last time she got upset about my boots.
Leliana: I mean the Inquisitor. 
Cullen: 
Inquisitor: Leliana thinks you are screwing me over the war table every night when you are forcing me to read you fat boring history books. I'd rather you did. 
Cullen: *teleports to Anderfels*
Leliana: Maker! You WERE reading the books there! 