No, doubtless is an adverb, not an adjective; in the above two sentences you are using it as an adjective.Could I write as below?:
It is a doubtless case that this prisoner will be extradited.
It is the doubtless case that this prisoner will be extradited.
I can't think of any more adverbs that end in -less, though there may be some. I think that you could safely say that doubtless is very unusual in that it is an adjective ending in -less that can also function as an adverb. English is like that; you have to learn words one by one. Similarly, most words that end in -ly are adverbs, but not all of them; saintly, cowardly, kingly, etc.[....]
Could you cite an another example for adverb that ends with -'less'.
Can I assume that no article will precede the word that is adverb.
Please guide me.