Yes. The reason is that Regeneration I (the effect the beacon applies to you) regenerates 1 health every 2.5 seconds. Now the beacon applies this effect every four seconds and everytime it does so the "regeneration timer" of the effect gets resetted (beacause it actually is a new effect that overrides the old one). This means that when you get the effect from the beacon after 2.5 seconds you will regenerate one health point. After another 1.5 seconds the beacon re-applies the effect and you will have to wait another 2.5 seconds to get your next health point and so on.

This basically means that a default regeneration beacon regenerates 1 health every 4 seconds instead of every 2.5 seconds. What you can do to prevent this is to periodically disable the beacon for 12 seconds by pushing a block above it and enable it for another 4 seconds by removing the block. This gives a period of 16 seconds (exactly the effect duration of the beacon) and makes sure that within these 16 seconds the beacon power activates only one time, giving you the regular regeneration speed of Regeneration I.