It has been suggested that young pulsars, with ages less than a million years, are possible counterparts of some of the Galactic unidentified gamma-ray sources detected by the EGRET instrument on-board the Compton Gamma Ray Observatory. In this work, we compare different aspects of the EGRET unidentified (EUI) source distribution in the Galactic plane with those of the pulsar distribution. An EUI source Log N-Log S analysis is presented and compared with the Galactic radio pulsar Log N-Log S distribution. A number of systematic effects that could introduce errors to the EGRET Log N-Log S relation are discussed. A two-point angular correlation analysis of the EUI sources and Galactic pulsars is performed. We find that the global distribution properties of the plane EUI sources do not follow those of the young pulsar population. We conclude that even though a fraction of the EUI sources may have young pulsar counterparts, the majority of them follow a distribution that is similar to the molecular cloud distribution in nearby spiral arms.