No, it should not. We do not use Norton, but ESET SysInspector runs fine on all tested machines running Avast, AVG, and McAfee.
Also, ESET develops and distributes their NoD32 Antivirus software, which suggests ESET SysInspector was developed to run without conflicts with various AV software products.
To be sure, contact their support team or visit their forum which is quite active: