Let's say a PID is implemented and the errors are calculated using the sensor data, but the sensor data lags by certain amount of time because of the overhead. And the lag time is smaller than the sampling period, how well does PID performs? What I am thinking is that PID will calculate errors based on past data, and use that to control. How will using a Kalman filter to estimate the actual sensor data help?
A discrete controller cannot feel anything that might vary within a sample period, so don't be concerned about it. Even a lag of one sample period is very negligible as seen by the PID and any technique you might consider to compensate for it will be definitely an overkill.
The right question you should ask yourself is: "is my sample period selected correctly according to the characteristics of the plant I want to control?"
Anyway, for significant lags (i.e. in the order of several sample periods) affecting a system, there exist methods such as the Smith Predictor that come to help you out.