I had the Mirena in for a grand total of 5 days last year - had to have it removed after I got PID (I never get infections) and excruciating pain. After that, I REALLY did my research.
To find out if Mirena has an impact on NBE, you have to look at the mechanics of Mirena. The actual way in which it prevents pregnancy is not known but it is known that Mirena (unlike the copper IUD) releases progesterone into your system. That's what keeps you from getting your period 3 - 6 months after insertion, if you are the "normal" user Bayer expects you to be and not one of the 1% like me whose body refused the device.
Some NBE tactics - mostly herbal ones - could, in theory, impact the effectiveness of birth control as they affect hormones. It would be hard to find a doctor to ask about this since most doctors have little to no knowledge when it comes to herbs and you'd have no easier time finding a naturopath who understands the mechanics of Mirena.
From the Mirena FAQs:
Mirena slowly releases very small amounts of the hormone levonorgestrel directly into your uterus.
There is no single explanation for how Mirena works. Mirena may:
* Thicken cervical mucus to prevent sperm from entering your uterus
* Inhibit sperm from reaching or fertilizing your egg
* Make the lining of your uterus thin
Mirena may stop the release of your egg from your ovary, but this is not the way it works in most cases. Most likely the above actions work together to prevent pregnancy
That being said, the hormonal function of Mirena doesn't seem to be the "only" function (like it would be in the birth control pill) as there are some theories that the actual structure of the IUD can prevent pregnancy on its own (which is why it can be used as emergency contraception if inserted within 10 days of unprotected sex).
So long story short, NBE with herbs probably wouldn't have an impact on Mirena's usefulness (not sure about vice versa as you are dealing with lab chemicals versus herbs) but it would be wise to be careful when mixing lab progesterone and herbal hormonal treatments. Just my (totally unqualified) $0.02, I'm not a doctor nor herbalist.