Yes, if you set it up like I have (in bridge mode) you should be able to share your home connection just like you were in a hotel room.
Basically what "bridge" mode does is tell the APE to act as a "bridge" spanning the wired and wireless networks. It does not do any address translation (NAT) nor attempt to give wireless devices IP address (DHCP). To the hotel it would look like all your wireless devices are plugged into your network connection, at once! While some network equipment could be sophisticated enough to detect this and shut your connection down, most aren't. Most hotels have some sort of welcome page where you agree to their terms to use their internet service, you should see this page on each device you connect up with and use, each device should then get a network address from the hotel's DHCP servers. Some hotels make you sign back on daily, some every few days.
If you had a wifi-only device like the iPad, and the APE, you should be able to use the hotel's connection anyway. If you were on vacation with your family and everyone had their own laptops, then everyone should be able to share and use that one ethernet jack in the room!