100% cool, for Eames or for Arthur (though of the two Eames is the least likely to ???? about it, his introduction to dreamsharing was uhhh different than Arthur's
But yes like people can go too deep and get caught in Limbo, Limbo creatures can sometimes venture too shallow and get caught in the waking world. Some intentionally, some not.
Since they're more likely to 'fall out' when there's more dreamers and given the brief comparisons of dream dens to opium dens, what's one more body of someone who looks not all there like he's not sure where he is? You clearly miscounted customers before.
(Also if Eames is feeling particularly kind the fake dating can continue with Cole being pulled out of the dream and Eames covering for him as no he's definitely a real person uhhhhhh that's my bf yeah.)
And yes helpfully because they are Dream Creatures, projections will always assume they belong there and are one of them. (Sometimes they do like to watch the dreamwalkers and just seem like more projections then too, unnoticed)
Kate
Gabreel
Alanna
Torii
Zepar
Arthur
Maison
Anne
Hux
Amanda
Arthur
Phasma
Claire
Gabreel
Sebastian
Alanna