Yes, blanks have souls.
The terms blank, pariah and untouchable are currently interchangeable. It's related to the 'Pariah gene', which is what gives them their ability.
Some of these individuals had degrees of immunity to psychic powers
and the energies of the warp; some - known as Untouchables or Blanks -
had fields so powerful that their presence disrupted the powers of or
wounded psychic beings
- Atlas Infernal, by Rob Sanders, page 284
and from just further up that page:
Clone embryos, gene sequenced from blacksoul null-stock
In the collection of short stories "Tales of Heresy", in the story "The Voice" by James Swallow, three sisters of silence encounter a vision from the warp and near the end of the story it is revealed that they do:
'I have done terrible things to get to this place,' said the voice.
'Pacts and accords that have scarred my soul'.
'We are Untouchable' Leilani husked. 'They say we have no souls'.
'We have,' came the reply. 'Else I would have had nothing to burn, no
coin to pay my way here.'
- Tales of Heresy, The Voice, page 267
The pariah gene merely blocks out the connection to the warp, giving the appearance of a lack of soul, but it doesn't actually stop them from having one.
The grey Knights codex states about Culexus assassins:
Culexus Assassins are primarily chosen because they have or appear to
have, no presence in the warp - they are, to all intents and purposes,
- Codex: Grey Knights, page 53
The 40k rules book expands on the information about these assassins:
Culexus Assassins, by far the rarest, are chosen from those few
individuals who possess [sic] the Pariah gene, making them
null-entities in the Warp.
- Warhammer 40k rulebook, 6th edition, page 181