Do users use their arrow keys to cycle through auto complete search results?

I'm working on a webapp/site that allows users to sign up to training courses that is aimed at the construction industry.

The main users of the website are self employed tradesman and office admins who will be booking staff onto training on their behalf.

The search input on the site has autocomplete functionality and I want to know if it's necessary to allow users to cycle through the suggested results using their up and down arrow keys and hitting enter to select that result?

I feel like the majority of on site tradesmen will be using handheld devices and that office admins will likely use their mouse rather than using shortcuts and the arrow keys - meaning that it's potentially unnecessary.

Is there any evidence out there that suggests it's worth having this functionality enabled?

Thanks