They certainly could, and not only because of the user name.
In all Windows 2000/XP systems, those two directories were located at:
C:\Documents and Settings\User\Application Data
C:\Documents and Settings\User\Local Settings\Temp
(I've heard rumors that this naming was chosen deliberately, to force newly written programs to accept long file names in case "C:\Program Files" wasn't enough of a push.)
While those Windows versions are now mostly out-of-support, such paths may still linger in app configurations if the same system was directly upgraded from 2000/XP to Vista/7 and from there to Win8/10. They remain valid paths in modern versions, too, thanks to Windows creating hidden symlinks pointing the old names to new ones.
In general, a well-written program should always assume that any path might contain spaces, commas, apostrophes, and other funny things. They've been allowed in paths ever since "C:\My Documents" in Windows 95 – in 2021 they should be a baseline assumption, not a "surprise"!