Can you add datafile to tablespace that is in hot backup mode?

Yes.

SQL> CREATE TABLESPACE TRYDAT DATAFILE '/ORACLE/MYHOMDB/dbf01/TDMYHOMDB_01.dbf' SIZE 100M REUSE AUTOEXTEND ON NEXT 100M MAXSIZE 16000M EXTENT MANAGEMENT LOCAL;

Tablespace created.

SQL> ALTER TABLESPACE TRYDAT BEGIN BACKUP;

Tablespace altered.

SQL> ALTER TABLESPACE TRYDAT ADD DATAFILE '/ORACLE/MYHOMDB/dbf01/TDMYHOMDB_02.dbff' SIZE 100M;

Tablespace altered.

SQL> ALTER TABLESPACE TRYDAT END BACKUP;

Tablespace altered.