Does Drupal 7 support connecting to DB using MySQLi?
No. Drupal 7 does not come with Mysqli support. It only comes with PDO based drivers for MySQL, pgSQL and SQLite.

https://www.drupal.org/node/310070

https://www.drupal.org/requirements/pdo

See the files :


INSTALL.mysql.txt
INSTALL.pgsql.txt
INSTALL.sqlite.txt


to find out more about how to install using each option.

There are also many community provided solutions for connecting to other databases including MsSQL, Mongo and Oracle.

Have a look at the Drupal modules page for more information on database drivers

The core advantage of PDO over MySQLi is in its database driver support. PDO supports 10+ different drivers, opposed to MySQLi, which supports MySQL only.

If you are interested in the comparison between PDO and Mysqli there are many articles around including this one.