Very little can be told about John Donne from his poem "Death, Be Not Proud." A poem is a creative work, and one cannot assume that the implied voice of a poetic narrator represents the actual ideas and opinions of the poet. The narrator of a poem, like that of a novel is a literary construct. One can tell from the poem that Donne was well-educated, and had a sophisticated vocabulary. The final lines appear to be a statement of Christian faith:
One short sleep past, we wake eternally,
And death shall be no more; Death, thou shalt die.
From external biographical information, we do know that Donne himself was Christian, and thus this couplet does in fact reflect Donne's own religious beliefs, but we could not come to that conclusion without corroborating biographical evidence.