I think it depends on the content of the message rather than the means of sending it.
I have to disagree. The only way to determine the content of the message is to acknowledge it through reading. The typically vague use of subject lines in the corporate workplace don't help this any. If you're compelled to check that mail for any reason other than personal dedication, I think it should be technically be billable. A few posts up made a good point in that hourly workers are paid to work within certain hours and that really should be where it stops. If the worker is felt necessary beyond their normal hours, on-call arrangements need to be established to compensate the employee for these situations.
2.4 statute miles of surgical tubing at Yale U. = 1 I.V.League