No, but partly this depends on the application and end-user's usage. A typical checkout request requires five messages and responses between client and server, and each message is < 150 bytes.
When a server is not receiving requests, it requires virtually no CPU time. When an application, or lmstat, requests the list of current users, this can significantly increase the amount of networking FLEXlm uses, depending on the number of current users.
Also, prior to FLEXlm v5, the use of port@host can increase network load, since the license file is downloaded from the server to the client. port@host should be, if possible, limited to small license files (for example, < 50 features). In v5+, port@host actually improves performance.