Will a surge protector purchased in the United States work in Italy?

Yes, but it’ll be complicated to do so.

First, you’ll need to use a converter between the receptacle and your surge suppressor.

Next, if the device you’re powering is not European, you’ll need another converter between your surge suppressor and your device.

See here.

You’re probably better off buying a surge suppressor in Italy.

Absolutely, if you get this one from Amazon – Universal Power Strip/Surge Protector

but not your 60hz 15amp unit.

This was briefly addressed by@hungryguy but you will need a converter from AC to DC power. US electricity tends to use Alternating Current (AC) and Europe tends to use Direct Current (DC). You can plug your power strip and surge protector into the converter and then plug your converter into a European electrical outlet. You should be able to find these converters at wither office supply stores or a home improvement store.

@Kato yeah HungryGuy did say complicated . . . and probably more expensive than just getting a Universal power strip/surge protector as referenced above

@Kato !?! Europe tends to use 220 volt power while we use 120volt, and both are AC.
Nobody’s used DC for power distribution since Edison lost out to Westinghouse(Tesla).

You are correct you’d want a converter or better get the powerstrip recommended by @njnyjobs and get also the plug adapters recommended so you can plug it in over there.

Also most of Eurpoe uses 50Hz. I think the USA uses 60Hz. Get a converter that converts that, too.