It's been a while since I applied for my ATAS, but I don't remember them asking incredibly specific information about my funding (I probably just wrote student loans, self-funding, etc.). I more so remember having to tell them which classes I anticipated taking since I'm doing a taught masters. I don't think they looked at it too closely, either. My university wasn't on the list (I go to University of the Arts London), so I selected University of London since they look pretty close and no one ever said anything - another girl on my course did the same.
They state on the website: "You will not need to send us any original documents at this time, as these will be checked by the Entry Clearnace Officer when you apply for your visa (or caseworker when applying for an extension)." So as long as what you have on the certificate they give you somewhat matches the documents you plan to send in, you should be fine.
Then again, they might not have been looking too closely at mine since I'm getting a degree in Publishing. Even the guy at the consulate was baffled as to why I needed an ATAS and barely looked at the thing, lol.
Sorry that's not the most definitive answer, but I hope it helps a little!
