Starting a database on a replica server
There should be no problem to start the database. There are however some things to consider:


The databases have both the same name, unique name, and DBID. This can cause problems if you want to back them both up by RMAN.
The configuration of sqlnet will have the name server A. Therefore the database might not be accessible from another server.


So change the DBID and unique name (Check the documentation on these subjects) and check the configuration files of sqlnet (normally in the $ORACLE_HOME/network/admin directory) for references to server A.