Can a fast internet connection compensate for a slow server? If the sever is bottlenecking at `100kB/s` with a bandwidth of `A`, would it bottleneck at any higher speed with a bandwidth of `2A`? In another words, can a fast internet connection compensate for a slow server to any extent?

No. A server cannot become faster when you upgrade its link alone (if the link isn't the bottleneck). The possible throughput is the lower value of local throughput and network throughput.