ordaniel I'm unsure if the Bela mini would be as capable of doing this task when compared to the original.
Yes. The computational resources are the same.
ordaniel Would the 4GB of onboard memory in the original be needed for a task like this?
The eMMC can be faster than some SD cards, but that won't be a problem when performing a convolution, as you will need your impulse response to be loaded in RAM at all ties, so the eMMC's read speed shouldn't come into play there.