You are correct in thinking that a microdermal anchor piercing doesn't go all the way through. Instead it is literally 'anchored' into the skin. However, it isn't a good idea to get a microdermal as an alternative to a standard monroe piercing. The area moves too much which means the piercing probably won't heal properly and will be much more likely to migrate or reject altogether. Microdermals are better suited to low-movement areas which allow the piercing to sit straight.
The good news is that a standard monroe piercing shouldn't affect your braces. The bar will be held in place by a flat disk which should sit flush against your lip and not interfere with your gums. An experienced piercer will be able to position the monroe so that it doesn't go anywhere near your braces.
As with all piercings there are risks to consider and I strongly recommend you do your research before deciding whether or not to do it. This page gives a basic overview of the procedure and healing of a monroe piercing as well as a guide to prices: [Link](Mouse over link to see full location)
You can also read about the risks involved when getting any piercing here: [Link](Mouse over link to see full location)
And here is some more specific information about the risks associated with lip piercings: [Link](Mouse over link to see full location)
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