Was the snake dead in the poem "The Snake" by D.H. Lawrence?

The snake in Lawrence's poem is very much alive when we first encounter it. The snake is before the speaker at the water trough, sipping the water; it "sipped with his straight mouth" and forced the speaker to wait "like a second comer" for the use of the water trough himself. The snake in this poem has no time to spare for human supremacy but makes use of the water trough as he pleases.
Later in the poem, the speaker feels that he should kill the snake, although he does not want to. However, when he throws something at the snake—"I think I did not hit him"—the snake withdraws into a "dreadful hole" still alive, and the speaker feels grateful in reality that he did not kill the snake, "one of the Lords of life," because he had not really wanted to kill it in the first place and only made aggressive overtures towards it because he felt he should.