Would a PCIe 2.0 X8 slot have enough bandwidth for a NIC with two 10 Gbps connections?
From what I understand, each lane on a PCIe 2.0 card is good for 4 Gbps, so 8 lanes = 32 Gbps, right? Is my math correct?
Your math is correct. I doubt you'll be able to max out both connections in both directions regardless, but the PCI-E bus to the network card won't be the limiting factor.
You should double-check to make sure your motherboard doesn't have choke points between the CPU and the slot though. For example, if they share a PCIe 2.0 x8 path with the hard drive controller, that could be an issue.