Web application: Do users use the arrow keys to scroll through the full automatic search results?

I am working on an application / website that allows users to enroll in training courses aimed at the construction industry.

The main users of the website are freelance merchants and office administrators who will reserve staff to train on their behalf.

The search entry on the site has an autocomplete function and I want to know if it is necessary to allow users to scroll through the suggested results with the up and down arrow keys and pressing Enter to select that result.

I feel that most of the merchants on the site will use portable devices and that office managers will probably use their mouse instead of using the shortcuts and arrow keys, which means that it is potentially unnecessary.

Is there any evidence to suggest that it is worthwhile to have this functionality enabled?

Thank you