How does Photon get the images?

Also, what would happen if Photon encounters a 404 when trying to retrieve an image? Would it just try to cache it the next time the page is loaded or would it cache the image as a broken image?

caching is triggered after the images are on all the application servers

I’m afraid there is no option to delay Photon in your Jetpack settings: it’s triggered as soon as the page containing Photon URLs is loaded. If you use auto-post plugins like Publicize to publish your posts to Social Networks immediately after publication, then the first page load happens only a few seconds after the post has been published.

To solve this issue, you’d have to create a function to disable Photon for a few minutes after the post has been published. This tutorial should help:
https://ethitter.com/2013/07/disable-jetpacks-photon-module-in-specific-situations/

figure out how to force Photon to pull the images from a specific IP.

You can catch all Photon requests if you can filter requests by User Agent and redirect Photon to a specific IP. Photon’s User Agent is Photon/1.0 (reference).

what would happen if Photon encounters a 404 when trying to retrieve an image?

It would cache a broken image until the next page load, and then attempt to cache the image again.

I hope this helps.