It’s still a fingerprint, the most vague information correlated with other data points can make a useful fingerprint. This is how a lot of the companies can track you even if you aren’t logged in, you using any service creates a pattern that with enough aggregate data can be used to approximate who you are.
As for the data transfer costs, any network data originating from AWS that hits an external network (an end user or another region) typically will incur a charge. To quote their blog post:
So you won’t be charged for incoming federated content, but serving content to the end user will count as traffic exiting AWS. I am not sure of your exact setup (AWS pricing is complex) but typically this is charged. This is probably negligible for a single-user instance, but I would be careful serving images from your instance to popular instances as this could incur unexpected costs.