Do I need my North American iPad’s charging block in Italy?

You'll need to check the specifications of the Power Adapter.

The acceptable AC supply range should be printed on the back. The illustration, if applicable to your actual Power Adapter, specifies input @100-250V - although, interestingly, it states "USB Input" (which clearly it is not!) and "This adapter does not convert voltage". As such, I might question the suitability of this item being used at all with expensive devices.

All Apple iPad USB power adapters are designed for use with power sources rated to provide 100V AC to 240V AC at 50Hz to 60Hz.  Apple iPad USB power adapters also comply with the IEC/UL 60950-1 and IEC/UL 62368-1 standards for use with power sources rated to provide 115V AC at 400Hz (typically found onboard commercial airlines).

If your Power Adapter supports European 220-240VAC in addition to US 110VAC supplies, it will be fully usable when travelling internationally. You may, however, require a simple pin-adapter to allow the Power Adapter to be used with AC power outlets in different countries. For example, a US flat 2-pin connector will require an adapter for the standard European round 2-pin socket - or UK 3-pin square socket. Travel adapters are readily available.

Which model iPad? Identify your iPad model - Apple Support

Which model Apple Charger? About Apple USB power adapters - Apple Support

You can use either a US charger and an adapter for the electrical connection pins in the socket, or can use a shaver socket present in various hotels (most chargers are multi-voltage, dual-frequency), or can use a locally-acquired ISB-A or USB-C charger.

The Apple charger you are using will show the accepted voltages and frequency input, and all I’ve encountered in this decade have been multi-voltage and capable of 50 and 60 Hertz frequencies.

Some Apple chargers have a removable so-called “duckhead” that makes the electrical connection in the power socket, and Apple sells “duckheads” with other pinouts.

The VYLEE shown as USB-A and USB-C connections. No mini - or micro-USB is shown.

That particular VYLEE charger is also good for roughly ~15 watts on USB-C. It doesn’t have all that much output wattage provided, as various iPad models can prefer 20 watts for charging.

That charger also can’t run all that many USB-A and USB-C connections simultaneously, given the 3.4 amp limit. It’s pretty close to one USB-C connection, in practical terms.

Your existing Apple Power Adapters are fully usable internationally. Simple pin-adapters, converting US flat two-pin to other world standards, are easily available - particularly so at Airports.

Alternatively, you might consider purchasing a suitable Apple Power Adapter at your destination. This provides an additional Power Adapter that can connect directly to the local supply - and is equally usable worldwide.