From what I saw of a quick look at their site, Algolia is capable of crawling your site so it should be useable with hugo as you normally do not have any backend because hugo generates static content.
To make it work you would have to sign up for an account at their site and then integrate the front end code into your theme, including a textbox for searching. Normally they have docs at their site which show ho to integrate the box into your site, so the only thing you also must do is to figure out how to integrate the necessary controls and code into your used theme.