Does codeigniter 3 support PHP 7?

yes codeigniter3.1.11 support PHP version 5.6 to latest 7.3.

Yes. The latest v3.0.4 changelog explicitly has changes to use PHP7 functionality where it can e.g.

Updated Security Library method get_random_bytes() to use PHP 7’s random_bytes() function when possible.

Update August 2018 There's also items in the change log for 3.1.8 which relate to fixes for PHP 7.2, as well as 3.1.7 which specifically mention fixes for PHP 7