It seems query browser executes queries on separate connections, or something like that, so when you execute a INSERT/UPDATE/DELETE and then a SELECT ROW_COUNT(); query, the data from the latter will no longer be available to the function.
An easy fix is to just create a wrapper procedure.
DROP PROCEDURE IF EXISTS `test`.`rc_exec`$$
CREATE PROCEDURE `test`.`rc_exec` (IN command VarChar(60000))
SET @query = command;
PREPARE stmt FROM @query;
SELECT ROW_COUNT() AS 'Affected rows';
Which you could then call like:
INSERT INTO myTable(First, Second)
VALUES ('Testing First', 'Testing Second'),
('Testing First again', 'Teststing Second again');");
Which returns a single field for 'Affected rows' with the value 2.