Staying in the area on two back-to-back visas is completely legit and is in fact discussed in the Handbook for the processing of visa applications and the modification of issued visas:
Example: A Moroccan lawyer representing a gender equality NGO who frequently
participates in meetings in various Member States holds a multiple-entry-visa which expires
on 31.5. She applies for a new visa on 15.4.If a new visa is issued, it should be valid from 1.6. and in such a case the visa holder would be entitled to enter the territory of the Member States on the basis of the first visa that will expire during the stay and leave on the basis of the new visa.
Entering through Italy is not needed either but it’s a little odd to have applied there if your next trip was to Greece (are you expecting to visit Italy regularly in the future perhaps?). It’s not relevant in this case since you had the visa already but the Italian consulate could (should?) have refused to issue it.
That said, as Karlson wrote in his comment, it’s a bit of a corner case so border guards might be unaware of the rules.
I’ve contacted the consulate of Greece regarding this question. The response from the Greek consulate was:
Consulate General of Greece in New York
11:28 am (1 day ago)I understand the problem now. You should contact the Consulate that issued the visa. He might have a problem if he continuously stays in Schengen.
Sincerely,
Consulate General of GreeceME
Sent: Τρίτη, 4 Φεβρουαρίου 2014 1:30 μμ
To: Consulate General of Greece in New York
Subject: RE: Visa Question
I apologize may be I didn’t make it clear the question is actually whether he can remain continuously in Schengen area.
On Feb 4, 2014 12:54 PM, “Consulate General of Greece in New York” wrote:
If the visa is valid then he can use it. You should contact the Consulate that issued the visa as well.
Sincerely,
Consulate General of Greece
Sent: Δευτέρα, 3 Φεβρουαρίου 2014 10:03 μμ
Subject: Visa Question
I have a friend who has 2 short term visas granted to me which turned out to be consecutive single entry visas.
Namely, One visa ends on May 2nd and the other begins on May 3rd. How he managed to achieve this I am not sure.
He has a question on whether or not he can continuously remain in Schengen area and what he will need to do to update the information?
He is arriving to Germany on April 19th for the first time in years.
My guess based on the comments received from German and Greek consulates is that consecutive visas is a rarity or should not be issued at all.
Given that I am responding after your intended visit days you might want to add what you have actually done.
Credit:stackoverflow.com‘