@ChrisJ800 - depends on the type of autopilot. Older types would be limted in the amount of roll, pitch and yaw they could command (and as such should theoretically not induce LOC as long as you keep an eye on them). Modern types are "Full authority", and can theoretically command anything.
For an example of what pitot failure can do to an autopilot, check the Birgenair 757 case. During climb, the blocked pitot indicated overspeed and the A/P commanded nose-up to the A/P's limit of control - the overspeed warning continued, so the Captain reduced thrust manually and almost immediately stalled and never recovered.