You can pick files from any Google account. It does not have to be the email address you use to sign in here.
Your sign-in here decides which organization the files go into. The Google account you choose in the next window only decides whose Drive you are picking from.
Google lets the Library read only the files you pick, for about an hour, and that access is never kept.
To pick several files at once, click the first one, then hold Ctrl (Command on a Mac) and click each of the others. Then press Select. Google's window marks a chosen file only faintly, so a file can be chosen even when it barely looks it. After you press Select, the Library tells you how many files came in and names any it could not bring in. Up to 25 files at a time.