Do live chat widgets increase sales?

On considered purchases, yes. On low-value repeat items they mostly add cost and a support queue, and an unanswered chat widget is worse than none.

In more detail

The deciding factor is whether somebody answers within a minute during the hours it is shown. If that cannot be staffed, a good FAQ and a WhatsApp number outperform a widget that says ‘we typically reply within a day’.

What to do about it

Unclear delivery timing causes more abandoned carts than price.

Delivery is what a customer remembers, and it is the part most stores control least.

A refund handled well makes a repeat customer more often than a sale handled well.

The mobile app angle

An app makes the after-sale part easier: order status, reordering and support in the place the customer already has open.