Does Estimated Delivery use an order cutoff time in PrestaShop?

Yes. Estimated Delivery Date has a single daily cutoff hour setting, in 24-hour format, and it works in a straightforward way.

• Order at or after the cutoff hour - the module adds one extra processing day, because that order won't make today's dispatch. The estimated delivery date on the product page shifts forward accordingly.
• Order before the cutoff - the product page can also show how many whole hours are left, e.g. Order within 3 hours, to nudge same-day dispatch.

On top of the cutoff, the date is built from a configurable number of processing days and automatic weekend exclusion (Saturdays and Sundays are skipped, and a date that lands on a weekend rolls to Monday). You choose the date format shown to customers.

The install defaults are enabled, PROCESSING_DAYS=1, CUTOFF_HOUR=14, weekend exclusion on, and DATE_FORMAT=l, F j. With those defaults, a Monday visitor before 14:00 sees the next eligible business day; a Monday visitor at or after 14:00 gets one extra processing day added before the date is displayed.

The module renders in the displayProductAdditionalInfo hook, so it appears only if the product page theme still calls that hook. It does not inspect the selected carrier, delivery country, warehouse, stock status or individual product lead time. The calculation is global for the shop and based on the server-side current time when the product page is generated.

Two honest limits worth knowing: the cutoff is a single store-wide hour - it is not per carrier or per country - and the hours left figure is whole hours, refreshed when the page loads, not a ticking second-by-second timer. If a global order-by-this-hour-for-delivery-by-this-date message on your product pages is what you need, that is exactly what this module does.