It doesn't appear that CSVREAD is requiring admin rights per the documentation. However CSVWRITE properly throws an error if I try to execute this as a standard user:
Exception in thread "main" org.h2.jdbc.JdbcSQLException: Admin rights are required for this operation; SQL statement:
CALL CSVWRITE('c:/temp/test.csv', 'SELECT * FROM TableA'); [90040-176]
at org.h2.message.DbException.getJdbcSQLException(DbException.java:344)
at org.h2.message.DbException.get(DbException.java:178)
I am using H2 version 1.3.176.