I've been enjoying my Europiccola that I bought on ebay about two months ago. It's a millennium, from about 2010. When I add water and turn it on from cold, most of the time it heats and then the light turns off (prompting me to release the false pressure). However, sometimes the light does not turn off before the pressure release valve opens, which I can see and hear operating. Is this normal?

Yes, it's normal. It should reduce the air pocket. In normal operation it opens briefly and then closes as pressure builds. You may also notice it opening and releasing some steam as the machine cools and pressure reduces.

If your machine has the anti-vacuum safety relief valve, then it has a very simple mechanism that is open when there is no pressure in the boiler. Once steam begins to go through the opening the pressure forces it up and it seals. When the pressure drops, gravity, possibly with a little help from the vacuum created inside the cooled boiler will open it again. When the machine is building pressure you may hear a little hissing that suddenly stops. This happens well before the machine comes up to full pressure. There are actually two valves in there, the tiny AV valve and the bigger spring-loaded safety relief valve. The safety relief valve should not be opening.

If you have a machine with this anti-vac valve, and if it's not sticking, you don't really need to bleed off the air ('false pressure') but no problem doing that if you don't completely trust your AV valve.

They are known to occasionally stick, and cleaning and reassembly may help with that. Also by taking apart the safety valve you will know for sure whether or not your machine has it (early Millennium machines did not.)

See this recent related thread for info and pics of that AV/Safety valve:
New La Pavoni Professional Lusso safety valve emptying tank at 0.25bar