If I'm going on vacation, is the best way to avoid a lower percentage response time to set my status as away?

Marking yourself as away just removes the penalty for not responding to new requests quickly. It does not affect your current or pending bookings,and it does not prevent you from booking new stays. It adds a note to your profile informing clients that this sitter is currently set to away mode and may not respond to messages, but they are still able to message you if they choose. This is exactly what you want to do if you'll be unable to reliably respond for a period of time.

If I'm not mistaken, I believe that this will simply prevent future incoming messages. Your profile will show an "Away" icon for the services that you offer so that potential clients are aware that you are currently unavailable. It should not affect current conversations or future booked stays. An alternative to setting yourself as away would be to simply mark the days that you are going to be out of town as unavailable on your calendar.