As far as I know Norton Internet Security does have the ability to detect and remove spywares, like Windows Defender does.
I'm not aware of any conflicts they might have, but in most cases when you have 2 active anti-spyware programs (they both actively tries to find spyware while you work) they might detect the same spyware and might conflict.
In this case I would recommend using only one active spyware detection and schedule a complete scan on each product (not at the same time, of course) every day or week (depending on how paranoid you are about spywares
)