To a large extent, yes, the job with respect to -that- battle is done, unless things go wrong. The general will have colonels, be they combat command commanders, brigade commanders, etc, to fight the actual battle, he's going to be thinking more about things beyond the influence of those subordinates. What's going on in the deep fight in the division's (Corp's, Army, Army group) sector, what opportunities may be opening up, what risks are being discovered. How things to the left or right might affect the battle he's currently involved in.

If things do start going wrong, the better the general's staff, the less work he has to do, as long as he has provided sufficient guidance in the planning process. A general may have what are today called "Commander's Critical Information Requirements", defined as information which is required to drive a decision. They're not 'nice to knows', these are questions which have been identified ahead of time as things which must be brought to the commander because it will determine a choice between action A and action B. Hopefully A and B have already been wargamed as branch plans and the staff will apply accordingly, but the general may have a veto. Note, CCIRs exist even if everything is going right, but the 'what to do about it' is almost always pre-ordained in such a case.

If something unexpected happens, the general will give guidance to the staff as to how to react. It may be as simple as "give priority of artillery support to that brigade" or it may be an entire reconfiguration or even cancellation of the plan.