A quick test suggests that the CSS for the old UI still works on the mobile browser login, which suggests to me that the mobile browser login is disconnected from the whole theme-based architecture?
Short version: should I invest in slapping together some styling to handle mobile browser logins, or will this be fixed at InstructureCon?
Authorial aside: mobile browser logins are going to keep happening until the Canvas app is useful for teachers.
You are correct in that the Theme Editor itself doesn't support the mobile login, just the browser version. However, customization for the mobile login can currently be made through a custom CSS file (the regular one, not the mobile one). More information about the clarification of each css file has been made in the discussion that you previously linked.
During Instructurecon this came up. There will be three new apps - Parent, Teacher, Student - to replace the current app (and speedgrader). Those new apps will pull in the branding already set in the New UI theme editor. If I remember correctly (I unfortunately can't find my notes on it) Parent is coming soon, then the other two will follow later (I think early next year).
Since Anthony was the one to say it (and not me), I can now change the answer to this question. The apps will support more branding options, but until then you'll still have to apply mobile styling in your regular CSS file.
Here's what's working for me right now.
In fact, I notice that the web login does have a conveniently styled body tag: body.ic-Login-Body
Weird how the mobile login seems to just be hacked together and ignored.