either with a forced error and parsing the error text
try
tell application "Mail"
some mailbox as text
end tell
on error e
set {TID, text item delimiters} to {text item delimiters, quote}
set mailboxName to text item 2 of e
set text item delimiters to TID
end try
mailboxName
or collect the path recursively
tell application "Mail"
set theBox to some mailbox
set thePath to name of theBox
repeat
try
set theBox to container of theBox
set thePath to name of theBox & "/" & thePath
on error
exit repeat
end try
end repeat
end tell
thePath