You're Correct!

The position of your arms and their alignment in your set up position, has a very big influence on how the club head will strike the ball and also the direction that the ball will be hit in.

Your arms need to hang down under your shoulders so that they are parallel to the target line, without one being more forward of the other. Achieving this position will allow you to swing the club head back from the golf ball along the target line. Once you have completed your back swing you will then be able to swing the club head back towards the ball and along the target line through impact. If your club face is square to the target as you do this, you will produce a straight, accurate golf shot.

Your arms should also be dangling vertically underneath your shoulders. Allowing your arms to dangle freely and naturally from your shoulders will encourage them to return to this position through impact. If you began with the club face centred to the golf ball, swinging from this position with your arms will allow you to return the club face back to the golf ball in a centred position and you will strike the ball from the sweet spot (centre). Striking from the centre of the face produces accurate golf shots of maximum length.

To create the correct position for your arms try the following drill. Stand parallel to the target line with your toes, knees, hips and shoulders. Place an alignment pole down your back, inside your t-shirt and tuck it into the top of your trousers. Stand up straight so that your head, middle of your shoulders and bottom of your back are all touching the pole. Tilt forward from your hips towards the target line, keeping these three points on the pole. Keep your shoulders and hips parallel to the target line as you do this. Tilt forward enough so that your arms hang freely and away from your body. Soften your knees. Hold this position for five seconds to train your body with the position and then relax. Keep repeating this exercise in sets of five, throughout the day.
The opposite is true if you set up in a position where your arms are too close to your body initially. Your arms will return to a more natural position further away from your body and produce a shot that is struck off the heel of the club face.

Off centre strikes produce inaccurate shots and loss of distance.

If you set up with your left arm more forward than your right, your shoulders will now be aiming to the right of target. This will cause you to swing the club head back on the inside of the target line and you will return the club head from the inside of the target line. This will produce a shot that travels directly to the right of target if your club face is square to the in to out swing path, or if you have a slightly closed the club face to the swing path through impact, you will see the ball start right of target but then curve left and finish left of target.

If you set up with your right arm more forward than your left in your address position, then your shoulders will now be aligned left of target and this will produce a back swing that moves outside the target line away from the golf ball. As you now swing the club back down towards the ball your swing path will be out to in, meaning that the club head is moving from the far side of the target line towards the nearside. If your club face is square to this direction of movement, you will hit the ball straight left of target. If the club face is slightly open to the swing path, you will see the ball start left of the target and then curve to the right, finishing right of target.

If your arms are too far away from your body at set up, then you will take the club head away too much on the inside of the target line on your back swing. When you return the club back towards the ball on your down swing, your arms will want to return to a natural position where they are hanging underneath your shoulders. This will result in you presenting the toe of the golf club to the ball, not the centre.