Is it possible to capture traces on a ChipWhisperer capture board using a non-ChipWhisperer target board, such as the STM32F4-DISCOVERY?
Absolutely- our own target boards are designed to make things easy, but in principle you can make modifications to generic target boards to successfully conduct side-channel attacks. You need to think about removing decoupling capacitors, getting access to the target clock, having some means of communicating with the target, and getting a useful capture trigger from it.
Whether this is possible or easy or hard will depend on the target of course.
The schematics for our targets are open-sourced, so you can look at them to see how we do this for our targets: