Quinn doesn't quite have invisible friends, but she does have lots of invisible animals — cats named Milo (after the co-lead in Milo and Otis, dogs, rabbits, the occasional pony, etc. She will run after them, catch them, pet them, cuddle them, and want you to do the same. If she forgets one in the car or outside or something, she can get quite distressed.
However, they have, upon occasion, proved to be helpful to have around.
Over the past few nights, when she's gotten a little distressed/distracted at bedtime, I've been able to pet Coll the collie and Point the pointer as they curl up in bed with her and convince her that they need her to stay still in bed because her dogs want her to make the bed warm. The coup de grace usually involves finding Milo sitting on the end of the bed, waiting for Quinn to settle down so that she can go to sleep.
Some nights it's worked better than others, but it's nice to know the invisible animals can be helpful ...