Some will, some will not. It all depends on the device. An external SSD likely will as there is a logical and simple fallback behavior. Thunderbolt devices that will not fallback to USB are eGPUs, docks (specifically Thunderbolt docks, not USB-C docks that use only USB for data), RAID arrays, adapters to SATA/FireWire/whatever, and PCIe breakout boxes. If something is using Thunderbolt then it's quite likely because it has to in order to get the speed it needs to operate as intended. A fairly common portable drive will likely fallback to USB if there's no Thunderbolt because these are made to move around to different computers. An eGPU is a kind of device that needs the PCI protocol on the wire that only Thunderbolt supplies.
With the new USB 3.2 and USB4 this might be different. Those have greater integration with Thunderbolt, higher speeds, and potentially PCI packets on the wire like Thunderbolt does, which makes fallback to USB a more feasible option. USB4 blurs the distinction between USB and Thunderbolt since this is effectively a merger of the two. Since that's still a bit in the future as I write this there's still some speculation on how that will work out. Until then devices falling back to USB if the host does not support Thunderbolt will be dependent on the device.