Connecting 2 time capsules?

If you connect them with ethernet cable the cable should go from one of the upper three ports (output) on the first TC to the bottom (WAN/input) port on the second TC. Normally your internet connection will be to the bottom port on the first TC.

The Mac Airport app should show you whether they are configured correctly.

Using ethernet should be faster than wifi.

If a viable Ethernet connection was available to the second TC when you initially configured it, that's what it would have selected. If not, it would connect to your existing AirPort network as a client.

The Ethernet option is preferable, if connecting them that way happens to be convenient for your particular installation. It really doesn't matter though. Although wireless communications will always be subject to a number of environmental variables that can contribute to unpredictable operation, it will only be a limiting factor if your wireless environment is particularly poor and the client TC can't enjoy a reasonably strong connection.

Anyway to answer your question a wired connection is not necessary. If it's working the way you have it, it will continue to work, assuming there are no significant changes to its wireless environment.