When utilizing server-based database engines, a while is going to be consumed for communication. Since SQLite is serverless, will it allow it to be faster than server-based database engines?

I dont think this problem has with "Serverless" to complete, observe that the SQLite has a lot more restrictions than other known systems (Saved Procs, email sights ... Read here). Aside From The application program uses SQLite's functionality through simple function calls, which reduce latency in database access – function calls inside a single process tend to be more efficient than inter-process communication.

Take a look Comparison of relational database management systems