In https://ham.stackexchange.com/a/1068/9 it's shown that one can use
$$ r = \sqrt{I^2+Q^2} $$
to decode AM signals from a direct conversion receiver. It appears that, in this particular case, I and Q are interchangeable, thus the SDR doesn't care which is which.
Is this true, and for straight AM they can be switched without issue?
Are there other modes, such as SSB and CW, where switching I and Q wouldn't matter?
If I'm operating an SDR, what clues can I look for that would indicate a swapped I and Q?