Yes, but the server itself will not know how fast the player is walking.
Let’s say that there are two players, A and B. They both have speed 10. Player A changes its speed locally with your code, so its speed becomes 16. When player A walks around, the server and player B can see that player A is moving faster, but the speed value for the server will still be 10. This is not really a problem when the server doesn’t need that information though.
EDIT: If you’re not sure on some things regarding server replication, you can always create two game instances with the “start server” button on the test tab in Roblox Studio, after selecting two players. You basically start a game with that button where each window that opens is another player.