I haven't noticed speed improvement but I haven't been measuring either. I adopted Colemak mainly to stave off RSI which I started having problems with at 21. I selected Colemak over Dvorak simply because vim config and the learning curve were easier, but I think now perhaps I should have gone with Workman and a matrix board.
Posture is the most important thing. All of my problems were due to poor posture that bent my wrists unnecessarily. I didn't own or have the space for a real desk or chair, which allowed the situation to devolve pretty horribly. Keep your forearms level so your wrists can be straight. Get a wrist rest to place in front of your keyboard AND pointing device. Small, split boards like the ergodox are nice because they let you adjust horizontal placement so you're not turning your arms inward, and also don't have that giant block of numpad etc on the right that force you to reach way over for the mouse. If not something as radical as an ergodox use a 60% or tenkeyless at least. You don't need 104 keys as much as you might think. Avoid software that requires heavy use of awkward key chording, prefer modes and single keystrokes, and map your modifiers to be more easily accessible (classical Ctrl placement etc).