I don't think they literally use the plane to teleport, but I think Icarus may probably be far more linked to "Richtofen" than anything.
Our characters were, at first, on the Giant, whence Icarus could be found crashed onto the roof, alright.
But if the characters didn't use the portals since then, it's highly possible that they went all the way from Der Riese's facility to the Griffin's castle by their own.
The fact is that their plan was to use the Giant Robot to track Dempsey 1.0, and even though we can see Icarus in ZnS, I remain conviced that they used a portal to go to the island.
In SoE, well, he was watching over all the scenery, at least he knew what was happening. Is he Rapt, or the Kronorium helped, or someone else informed him? He's not alone after all, but whatever. Still, he knew what was to happen/what was happening here. After all he just kind of totally showed up just after we (SoE characters) sealed the Shadow's Man into the Summoning Key, and Rickyricky used a portal to pop up, hence the apparition of Icarus in this "theory".
I think that there is Icarus each time someone uses the portals, or something like that. Like this insurance policy Ed was talking about, as he always carry these blood vials around, which have been assumed to be relate to at least two of the mobsters with the obvious numbering written onto those.
More precisely, I think that this is the doings of Richtofen that "summons" Icarus, like if this was a way for him to "assure" something, or like the "side effect" of these 'doings', time travel/safety, after all he shows up at SoE and it was there, they showed up in The Giant and it was there (yes, he used a simple teleporter, but the others didn't, as it has been clearly said by Dempsey himself at the beginning of the game that he "jumped" ; plus I would have another explanation about them to follow this reasoning), if DE happens in the same dimension as The Giant, it probably doesn't "need" to be "there", or is not meant to be there "twice", therefore assuming that ZnS happens in a different dimension.
As for where it would be in Origins, well... Most likely a reason similiar to the DE's one.
After all "... MAXIS, HAVE YOU FOUND THE SPACE-TIME COORDINATES FOR THE OTHER INDIVIDUALS I ASKED YOU FOR... ITS IMPERATIVE THAT WE FIND THEM AS WELL... YOU MUST TRUST ME ON THIS... FOR MY PLAN TO WORK, WE NEED THEIR BLOOD" ; 'he' did imply that the blood of 'some' individuals are needed for 'this' person's plan to work. We can assume that this was from Richtofen... But actually, it may be "this someone else", such as the man who knocked at the door / M / etc. Then it could just... completely be a/the way to enable them to teleport through time and space without the use of the teleporters... Well, whatever.
That's just a simple theory about the blood vials/Icarus amongst all the others, there's plenty.
And plenty others that may contradict all the others.
The game is, so far, far too confusing and in disharmony between all the mysteries and the things we can confirm in proportion, right now, we can't do anything else other than theorizing...