pdath: I think you might be missing the point of going on Holiday in such a spot.
If the business was going to suffer without that small amount of daily input then a lot of people may say they can't go to that nice place but worth trying to get both.
I would be checking before I went that the type of connectivity available is going to be adequate. We know that a lot/most websites are no longer usable over dialup. Even mobile versions have bloated as the mobile bandwidth increases. Email plain text is small amount of data but a picture says 1000 words and unfortunately unless there is an intermediate server that is shrinking images that full resolution photo in the email just won't get through. Maybe some lean webmail clients will do better job.
If there is 3G nearby I would have thought that was a better option than dialup - at least seems it may be backup. Enjoy the holiday !