iZettle would not get a lot of adoption in it's current form.

For merchants the biggest issue around chip and pin cards is this:

If the merchant takes a signature, then they are liable for loss incurred by bad transactions.

Which simply means, very few merchant accept signatures and only in exceptional circumstances.

So any EMV reader in Europe, to achieve adoption by merchants, will need to offer a PIN entry method.

However here is the other part of the deal.

A PIN entry keypad must be secure. In fact, the keys themselves cannot be implemented in software that exposes the key presses to any other software.

Usually this means that the hardware keyboard itself doesn't send keypresses to the OS, it is a dedicated piece of hardware (with screen) that only transmits the hash of the PIN to any external system.

In effect, Square would need to re-design their device to include a PIN entry keypad and screen.