At minimum, the error should be logged somewhere, and not just vanished. At least you get to know how frequently it occurs if/when that becomes meaningful to you.
I have plenty of monitors to ensure my services are available (four-nines uptime for almost a decade). Internet unavailable errors are useless to log.
Also, only do it for exceptions you think might actually hit there and you're OK with quietly squashing. Otherwise, please let something else try and handle it.