No, that link will always point to the most recent version.
For example, https://arxiv.org/pdf/1909.03562.pdf gives version 5 of https://arxiv.org/abs/1909.03562, as noted in the left margin of the first page.
For example, https://arxiv.org/pdf/1909.03562.pdf gives version 5 of https://arxiv.org/abs/1909.03562, as noted in the left margin of the first page.