I don't disagree with the possibility and plausibility of some arguments for vault a 17 jumpsuit.
We have elements of the East Coast Brotherhood of Steel that made it to the West Coast, plus the Enclave also, and, the presence of Super Mutants on the East Coast indicates a migration from the West since the original FEV dipping vats were in the West, the Super Mutants can't procreate, and the vats were destroyed.
It's thus plausible and possible for other things associated with the West side of the continent to wind up on the East side.
Arguments against this, however, also have merit.
The curve of the character's back from shoulder to shoulder in the angle of the source picture, combined with a slight ambiguity of the median vertical line on the characters back give enough wiggle room of ambiguity that the vault could very well read 117.
Additionally, since the game's setting is in the East Coast area, and vaults numbered in the 100s are the fashion for this area in the numbering convention established, there's substantial merit for a higher plausibility and probability for the jumpsuit to be a 117 jumpsuit.
There are additional arguments for both 17, and 117, such as 17 goods and material collected by wasteland scavengers who found the vault in the West making it's way into the Brahmin trader network and creeping from coast to coast, hand to hand, or meeting a former 17 resident that didn't grow so big during mutation as to rip the suit to shreds, that might even be available as a human/ghoul sized super mutant companion, potentially even with senses intact, and potentially available to use all the human and ghoul sized armors.
Occam's Razor is a little indifferent too. It looks like it reads 17, so it must be 17 ... or, 117 is East Coast, the game is on East Coast thereby 117.
Unless there's other concept art, in game footage, and/or something else that comes out of Bethesda that confirms one of these, it's likely we won't know for sure until we get our grubby mittens on the actual game.