I have built a Beacon - full pyramid using Iron Blocks.
It is completely solid. I then chose the buffs - Haste II, as well as Regen for having the full pyramid, then activated it using an Iron Ingot.
However, even though I have the Haste II status effect applied, (the icon appears in my HUD, and the counter refreshes every 3 seconds), it has not applied the Regen (no icons appeared on my HUD) and it does not seem to actually apply to my digging speed at all - I have tried with two different Picks, one with Efficiency V, and one without. It takes just as long to mine if I did not have the Haste II enchantment applied at all.