Yes, your connection will be faster but not the connection speed.
When you have a dynamic IP (not static) your pc uses a DHCP protocol to ask the server for an IP. This takes time, but once you have that IP, you are connected and the job is done. Usually this is so fast you don't even know it is there.
A static IP jumps that step because "that" IP is already yours to use.
The advantages from a static IP from a Dynamic is for instance if you are running a server. Some services (like online gaming) take advantage of a static IP because players can get back using the same address. If the IP changes, players loose the server. This is if the game is IP oriented, some games are not.
Another advantage has to do with cluttered networks. If you have a static IP, it's like having a reserved spot inside a garage. Even if full, that space is free for you.
Now, as for connection speed, it's the same unless there is something else on the game, like a contract clause or something.