I have not personally done it because who wants to go through the hastle. But it is possible according to the Italian web site.
http://www.italia.it/en/useful-info/covid-19-updates-information-for-tourists.html
If, on entering Italy, travellers do not present green certification or the negative result of a swab test, they can nevertheless enter the country but will have to undergo fiduciary isolation for 5 days and inform the Prevention Department of the competent area health authority (see page:
COVID-19 Toll-free numbers and regional information). After 5 days of isolation, they must perform an additional molecular or antigen test.