It depends on how much bandwidth each is using. There is a set amount of data each one can transfer, however the interface between the motherboard and ports is less than the sum of the max data transfer of the ports. As a result, when transferring more data than the motherboard interface, the data transfer rate in lowered so as not to exceed the interface bandwidth limit. So yes, one, or both of the ports, can be bottle necked if they are both transferring data at the same time (as almost max saturation).
Thanks. Is this common? If I connect one of the two Thunderbolt ports to a Thunderbolt 3 dock and then an eGPU from the dock, will each device get full performance? Is this way better than direction connection from the laptop's first Thunderbolt port to eGPU and the 2nd Thunderbolt port to Thunderbolt 3 (to access USB drives and 4K monitor at 60Hz)?
Use one Thunderbolt Port into the eGPU, as this will fully saturate the connection bandwidth. This will mean less bandwidth for the dock (monitor and storage) as there will be less bandwidth. If you plan on using an eGPU, get a laptop that isn't limited by output bandwidth, as by the sound of it you are going to need all the bandwidth you can get!