yes. I'm following the subject as I go to Italy every year, plus some other countries as a side trip.
It goes into effect tomorrow.
It will be valid for EU numbers, therefore if you buy a SIM card in Italy (with an Italian number) you won't be charged roaming fees if you straddle into France or Austria for a few days during your Italian visit.
There are some caveats. Basically it applies to basic package (promotional extra minutes/data may not be included) and it's valid only for temporary stays (so it won't be valid for an Italian who buys a SIM card in Italy and then moves to France permanently).
But for the purposes of you going to one country, purchasing a local SIM, then going temporarily into another it should work.
I'm going back at the end of the month, will have an Italian SIM, but also going into Switzerland, so we'll see. Switz is not part of the EU, but apparently most mobile carriers will apply the rule to Switz. too (we'll see that one too).