Porting SuperDuper Backups

[lugesm]

Sorry if this is such an elementary (maybe even dumb) question, but I am new to the Mac and even newer to SuperDuper.

I have found that I can make a SuperDuper bootable backup of my iMac hard drive, carry the external HD where the backup is stored to my wife's mac-mini, and boot her machine from the backup HD.

My wife's mac booted from the external HD perfectly, albeit somewhat slowly. Everything on her machine was then identical to the operating environment on my iMac, as it should be. So far, so good.

However, my machine is Ethernet connected to the router, and her machine is connected through Airport to the wireless router. Given this situation, when I boot her machine from the SuperDuper backup from my iMac I am unable to access the Internet.

Question: If I boot her mac-mini from the HD with the SuperDuper bootable backup from my iMac . . . then make changes to such things as the Internet connection . . . does this in any way affect the contents of her hard drive which is (hopefully) completely inactive in this situation?

Further, I assume that when I later do a refresh to the backup HD on my iMac, SuperDuper will discover any changes made to the HD while on my wife's mini and correct those files to again match my machine.

My apologies if these questions are too dumb, verbose, or elementary. Appreciate any comments you can make.

Thanks,
L