Yes. In either case, there should be a clear message that the board is temporarily disabled due to load.
phpBB already distinguishes between a board disabled manually and one disabled due to load settings in the language presented on the board index to guests. If a load setting has disabled the board the language string presented is:
BOARD_UNAVAILABLE' => 'Sorry but the board is temporarily unavailable, please try again in a few minutes.',
That has always seemed fairly clear to me but that could be because I am very familiar with phpBB and know that when the board is disabled by an admin a different string is used:
'BOARD_DISABLE' => 'Sorry but this board is currently unavailable.',
I propose the best way to address the issue the OP experienced is just to be even more explicit in the BOARD_UNAVAILABLE string, instead of "Sorry but the board is temporarily unavailable, please try again in a few minutes." how about "Sorry but the board is temporarily unavailable , please try again in a few minutes."
That should provide sufficient detail to any non-logged in users/mods & admins. For admins/mods who happen to be logged in when the board goes offline or have persistent logins you can add a warning or notice box on the ACP index (similar to the install folder or config.php permission checks) that displays the BOARD_UNAVAILABLE message.
Also now that I am looking at the language strings I see some annoying inconsistencies and word choices that do not accurately convey the situation.
Personally I would refine the language strings as follows:
'BOARD_DISABLE' => '
Sorry but This board is currently unavailable.',
'BOARD_UNAVAILABLE' => '
Sorry but the board is temporarily unavailable , please try again in a few minutes .'
"temporarily" is a subjective label at best and you honestly have no way of knowing how long the the server resource issue will take to be resolved. By using the language you have now you create an expectation that the outage will be momentary when you have no information to base that on. Better to be conservative when setting expectations and report back the current state of the board, no more no less.