A good grip doesn't automatically mean that you'll have a good-looking swing, but it will help considerably. Many golfers struggle all their lives with grips which will never be conducive to good movements.
A poor grip will put too much emphasis on your hands because it will lead them to over-controlling the club and moving it out of position. Back in the days of hickory shafts good hands were required to control the flex and torque of those old clubs. Playing good golf with a dodgy grip is more than possible but these players who have technically incorrect grips get by through sheer talent, great hand-eye coordination and lots of practice, therefore they're able to compensate for any grip problems they might have.
The hinging and unhinging of your wrists are extremely important in transferring power needed to trigger the lever action the swing creates with your arms and club. The way you place your hands on the club is vital in producing effective consistent shots for example, if you hold the club too much in your palms the result will restrict the correct hinging or cocking of your wrists. On the other hand, a club held too much in your fingers will tend to make your wrists overactive and loose. So, take your time and start with your left hand and once it's placed correctly then bring in your right hand. Remember that your grip is not based on one hand or the other but rather a unit of the two.
Out of Bounds: In some cases, I quite like irritating golfers who need to be irritated.