Can I set a Timecapsule to connect to a wireless network, and hook up more network equipment to it with cables?
Yes - Time Capsule is a fully functioning Airport and you can bridge, extend or perform any other function of Airport networking as needed without regards to there being a hard drive inside the unit.

You needn't worry about changing the network topology and having Macs not find the backup. Even if you actually change the name of the Time Capsule or change the password needed to mount the drive - once you remove the old "Time Capsule" backup as a destination from each Mac, you can add it back with the new name and/or password and the system will know it's the same volume and continue backing up just as it left off - no duplication or other ill effects will ensue due to you changing the names / networking.



I do exactly as you propose/describe with one change. I have a new AirPort Express that wirelessly extends (dotted lines) my network and I hard wire it (solid line) to the Time Capsule that used to provide wireless extension. I then turned off the wireless on the TC and run it in bridge mode (it's basically a gigabit ethernet switch now that provides three ethernet connections for two servers and a NAS) so that it's part of the network and still accessible as a backup volume.