Speaking from a general ship (i.e. not just Star Trek) standard, no. You generally have different duty stations for a reason, and the helmsman is the position in question here.
A professional helmsman maintains a steady course, properly executes all rudder orders, and communicates to the officer on the bridge using navigational terms relating to ship's heading and steering. A helmsman relies upon visual references, a magnetic and gyrocompass, and a rudder angle indicator to steer a steady course. The mate or other officer on the bridge directs the helmsman aboard merchant or navy ships.
Now, Starfleet is a quasi-military organization. Still, you have a commanding officer in charge of the bridge. In Star Trek, a lot of these stations can be automated by computer (Star Trek III saw 5 people run the entire ship), but you still need orders issued by the commanding officer and carried out by the crew. A major reason for this is situational awareness. An order might be given that doesn't take into account the status of the ship. The helmsman's one job is to steer the ship and make sure they don't run into anything. In real life, a navy ship lost situational awareness and was struck by other ship as a result.
We do see commanding officers run the helm in unusual circumstances. In the episode 11001001, the entire ship is evacuated, except for Picard and Riker. At the end of the episode, once the problem is resolved, we see Picard enter coordinates and engage the helm by himself, partly for pragmatic reasons, and partly for comedic effect (Picard tells himself to "engage").