Can MariaDB connector (driver) be used instead of the MySQL connector (driver) when connecting to AWS Aurora cluster MySQL instance?
Yes. I've personally used neither the MariaDB Connector/J nor the MySQL Connector/J against AWS Aurora cluster MySQL. However, according to the MariaDB documentation on its Connector/J - my emphasis:
MariaDB Connector/J is used to connect applications developed in Java
to MariaDB and MySQL databases using the standard JDBC API. The
library is LGPL licensed.
So, MariaDB's Connector/J officially supports MySQL databases, and Amazon Aurora MySQL is supposed to be a drop-in replacement for MySQL.
Also, note that according to the same documentation, MariaDB Connector/J has a special 'aurora' failover parameter. See MariaDB's Knowledge Base article Failover and High availability with MariaDB Connector/J for more details.
I've not found anything specifically mentioning Aurora in the MySQL Connector/J documentation, so it would seem MariaDB's connector could actually be a better choice.
It should also be mentioned that the licences are different: MariaDB Connector/J is LGPL v2.1+ and MySQL Community Connector/J is GLPv2 with a few additions.