From Mechanical Database
Once removing the intake snorkel as many other Neon owners have done, no power gain was noticed at all, but rather a loss in power. Several runs at Neon97 (in a 97 DOHC ACR Coupe) were performed with and without the snorkel. Although the results weren't extremely obvious, the car didn't seem to move faster, rather sometimes even slower without the snorkel.
Another suspected culprit behind the decrease in performance was the increase in IAT (intake air temp) if the snorkel was removed. An experiment was attempted, where the ACR Coupe was driven at a steady 60 mph over a given distance of 3 miles, and the IAT monitored by using DRB III at the end of the run. The IAT readings were compared with and without the snorkel over the course of 6 runs. The results were yet again not extremely obvious. Sometimes the IAT increased with the snorkel removed, other runs it didn't.
Another theory is that the snorkel directs the air flow in a more linear way to the air box. Perhaps removing the snorkel causes less air to go to the air box due to turbulance. This turbulance could be causing the air box to resonate, producing the noise, a loud and deep sound. Making some owners mistake the increase in sound for performance.