having a data connection will speed up the process of locking on gps satellites, I usually use my home wifi connection to obtain a lock before leaving for a journey. but GPS itself doesn't require data connectivity to work.
and as far as difference in reading on gps is concerned, it is usually less than what we see on the speedo, (depending on the tire size you are using and calibration of your vehicle's meter, it could be more as well)
but I have found the readings of gps comply with speed cameras of police both times i got a speeding ticket