Not really, you still need part J and distances between combustible sources.
Op is installing a free standing stove.
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Not talking about distance between combustibles, discussion is regarding differences between stoves fitted in fireplace recess and free standing where there are different rules.
OP hasnt said stove is free standing but this looks like in fireplace??....
If you need to extend the depth of the hearth over the current floorboards then I was thinking that the cement board would give a base area that can be cut to size and even notched so you can get it all the way into the fireplace opening