The answer is yes.
We can display/highlight public holidays in F4 help for date based on the country calendar.
This can be done by assigning factory calendar Id to the function module “F4_DATE”.
Before assigning the factory calendar id, the F4 help for date is as below.

Here is the sample code -
PARAMETERS p_date TYPE workflds-gkday.
AT SELECTION-SCREEN ON VALUE-REQUEST FOR p_date.
CALL FUNCTION 'F4_DATE'
EXPORTING
date_for_first_month = sy-datum
factory_calendar_id = 'IN' " 'IN' for India
IMPORTING
select_date = p_date
EXCEPTIONS
calendar_buffer_not_loadable = 1
date_after_range = 2
date_before_range = 3
date_invalid = 4
factory_calendar_not_found = 5
holiday_calendar_not_found = 6
parameter_conflict = 7
OTHERS = 8.
IF sy-subrc <> 0.
* Implement suitable error handling here
ENDIF.
Output:
Execute the program and press F4.

In this way, we can highlight the holidays based on the country in the date input help.
Note: We can see all the factory calendar ids at the transaction SCAL.