Consider the following:
INSERT INTO prp_property1 (module_name,environment_name,NAME,VALUE) VALUES ('','production','','300000');
/** Assume there is syntax error SQL here...**/
Blah blah blah
DELETE FROM prp_property1 WHERE environment_name = 'production';
No, transactions are not rolled back as soon as an error occurs. But you may be using a client-application which applies this policy.
For example, if you are using the mysql command-line client, then it normally stops executing when an error occurs and will quit. Quitting while a transaction is in progress does cause it to be rolled back.
When you are writing your own application, you can control the policy on rollback, but there are some exceptions:
Other than these conditions, if you invoke a command which generates an error, the error is returned as normal, and you are free to do whatever you like, including committing the transaction anyway.