Custom product/order field: can this be set by the system?

I have a client trying to do online bookings for events with a lot of different dates, so it isn't a desirable solution to create a hika characteristic for each date because some dates become unavailable over time or don't apply to certain products.

I was wondering if there is a way to create a custom field, which is set by the system based on a custom script and the user cannot change this field but can see it. The field would be displayed in the checkout as well as in the backend during order processing.

In your documentation there appears to be something like this in the business edition ("order custom field"?). Can this be configured to be unchangeable by the customer but changeable when placing an order?

Example:
30 events are added as products and each has its own set of date/times. Instead of setting up a characteristic for each event/date, an external database would contain all the events and dates, and a custom script would list these dates on the event/product page. The client would pick a date and the script/system would append this selection to the order as a custom field, which is displayed during checkout and backend.

ie. "Some Concert" occurs on "November 9, 10, 11". Customer picks November 10 and hits add-to-cart, when this is done, the script appends "November 10" to the custom field for the concert. During checkout, the customer sees something like "Some concert: November 10" and in the backend, the staff sees "some concert" with the custom field = "November 10"