Nope, won't start up if it can't find a signal. Why don't you just use Dish Anywhere either your iPad, aPad or laptop. You can access anything on the Hopper using that plus stream live TV (doesn't have to be on the Hopper) if your hotel room doesn't have that channel but you are subscribed to it.
I just tried booting my H3 with no satellite connection and was able to get to the DVR fine. Once the "acquiring signal" dialog comes up, just hit the DVR button.
There is a time limit after which Dish receivers no longer function without a "hit" from the satellite but I think it's more like a month.
Hopper Go, when available, would be a great option for what you are considering. For now, if you have a tablet (iPad or Android) you can DOWNLOAD programs from your Hopper before you leave.
DishAnywhere might work but with limited bandwidth you most likely wouldn't get HD quality video. Your home's uplink internet speed is also a factor.
An external hard drive must be connected to a Dish VIP or Hopper receiver to function since the files are encrypted.