Yes, it is possible to have the gap too small.
On my previous race car I changed the msd pickup and went to a digital 6 ignition at the same time and it developed a miss at around 5700 rpm and my tach being triggered off of the box would sometimes trigger the shift light at the wrong time. I thought the msd dig 6 box was bad and sent it back to msd. They found nothing wrong with it but did send me a new one anyway and I still had the problem. I made ground and power wiring changes but nothing helped. One day someone told me to turn the rev limiter off on the dig 6 and the car ran fine so I was still blaming the box again. Anyway it turned out that when I setup the pickup gap to .003" it was too close. I changed it to .025" and all my problems went away.
One thing you have to make sure is when you tighten down the msd pickup you don't over tighten it and crack it because it will cause a miss too. AND the magnet has to be oriented right.