Is hardware connections (i.e. CrossFire bridges) between GPUs for software operation required?
No, you don't need hardware connections (i.e. CrossFire bridges) between GPUs for GPGPU application. Starting from ~11.9 drivers AMD finally removed monitor-attached-to-each-card requirement, so now it's possible to simply pack several GPUs within one system and they'll work. Though mixing different families (really different, like 5970 == VLIW5 & 6990 == VLIW4) aren't that recommended.
Crossfire required only for graphics processing, i.e. OpenGL, DirectX applications where several GPUs working together to build separate frames of a picture, etc and they actively interchanging data with each other. For GPGPU applications we don't need to link devices together, we treat them as they are -- totally separate devices with separate resources. It were even problems with earlier Catalyst drivers when GPUs with hardware crossfire bridge weren't working properly for GPGPU.
All in all, general advice is to avoid SLI/Crossfire connectors when working with GPGPU applications.