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.