Honestly, I rank that long side libertarianism. It's the plea and cry of people wanting to avoid countability of their own actions to anyone they don't wish to, and unfortunately no one can be trusted to consequence themselves. I scoff at the use of conservative in that phrase. I myself am a conservative atheist, and with that said, I still maintain a general respect for religion. Some people can't handle existential depression and will fall victim to themselves without that trust of a higher power. I support this, as I support ANY positive reinforcement of a persons ability to be a productive member of society.
However, as a land that sponges up both religious and social practices, even if a general ruling could be established for each and every social and religious structure in America, it would all fall apart the moment that you apply group A to group B. It's practically sanctioning the existence of gangs! You need a government to establish order on the various factions that would spring up... and then... THEN... you no longer have conservative anarchy. Just like plain ol' anarchy, the moment you unleash it, it turns into a struggle revolving around "might makes right" which will culminate into dictatorship, totalitarianism, or any number of tangent governments from that.

Is it a good thing? Hmm... if you believe in 'purification by fire', then yes- and this would be the bonfire.

It is hard to say what conservative anarchism would be. Although i have heard the term before i have yet to see anyone outline what it is in practice.

So lets look at what a conservative is and what an anarchist is.

From wikipedia
Conservatism: is a political and social philosophy that promotes the maintenance of traditional institutions and supports, at the most, minimal and gradual change in society.

Anarchism is a political philosophy which considers the state undesirable, unnecessary and harmful, and instead promotes a stateless society, or anarchy. It seeks to diminish or even abolish authority in the conduct of human relations.

Although you could argue there are ways to fuse the two ideologies i would say in practice they are opposed to eachother. Since Conservatism wants to maintain traditional institutions and Anarchism is, in general, against institutions.

Now there is a movement called Anarcho-capitalism which does retain much of the current economic system while abolishing much of the state. This could be argued to be a form of conservative anarchism and would probably look something like Libertinism in practice.

Like all political ideologies there are pros and cons.

I would argue Conservative Anarchism, if it could be made into a coherent philosophy, would probably be useless in the real world. The internal conflicts of the philosophy would make it difficult to apply to real world situations and would probably leave use with worst of both worlds solutions.