Why I want to do this is that I understand that network throughput can be reduced dramatically for computers connected to the network-extending AirPort Express
"Client Mode" will use up more bandwidth than "Extend a wireless network".......another tidbit that Apple never bothers to mention to common folk.
If it matters, my Time Capsule that creates the wifi network is in bridge mode. It's connected upstream by Ethernet to a router that I can't control.
Matters a lot, since the upstream router is in charge of assigning a new IP address to the AirPort Express after any configuration change. At a minimum, you really need to restart the router after you make any kind of changes like this. If you can't restart the router, then power off the Express and try restarting the Time Capsule. Then, power up the Express again.
If you have a laptop, temporarily turn off the WiFi and locate it so that it is closer to the Time Capsule, then turn the WiFi back on and the device will usually pick up a signal from the closest access point.
If you are using the Express for AirPlay, the best way to connect the Express is via Ethernet back to the Time Capsule. Then, you can turn off the WiFi altogether on the Express and it won't be such a drain on the network.