Sim, Dumbledore pediu a Snape para matá-lo, então Draco não o faria.

“All the same, try. I am concerned less for myself than for accidental victims of whatever schemes might occur to the boy. Ultimately, of course, there is only one thing to be done if we are to save him from Lord Voldemort’s wrath.’

Snape raised his eyebrows and his tone was sardonic as he asked, ‘Are you intending to let him kill you?’

‘Certainly not. You must kill me.”
_{^{- Harry Potter and the Deathly Hallows, Chapter 33 (The Prince’s Tale)}}

Dumbledore não queria que Draco fizesse isso e prejudicasse sua alma, mas ele também não queria morrer nas mãos de alguém que prolongaria sua morte e a tornaria mais dolorosa. Ele preferiu que Snape o matasse rapidamente, e desde que foi feito como um ato de misericórdia, a alma de Snape permaneceria intacta.

“If you don’t mind dying,’ said Snape roughly, ‘why not let Draco do it?’

‘That boy’s soul is not yet so damaged,’ said Dumbledore. ‘I would not have it ripped apart on my account.’

‘And my soul, Dumbledore? Mine?’

‘You alone know whether it will harm your soul to help an old man avoid pain and humiliation,’ said Dumbledore. ‘I ask this one, great favour of you, Severus, because death is coming for me as surely as the Chudley Cannons will finish bottom of this year’s league. I confess I should prefer a quick, painless exit to the protracted and messy affair it will be if, for instance, Greyback is involved – I hear Voldemort has recruited him? Or dear Bellatrix, who likes to play with her food before she eats it.”
_{^{- Harry Potter and the Deathly Hallows, Chapter 33 (The Prince’s Tale)}}

Está claro que Dumbledore perguntou e esperou que Snape o matasse, e esse sempre foi o plano dele.

“After you have killed me, Severus –’

‘You refuse to tell me everything, yet you expect that small service of me!’ snarled Snape, and real anger flared in the thin face now.”
_{^{- Harry Potter and the Deathly Hallows, Chapter 33 (The Prince’s Tale)}}

Então sim, Dumbledore de fato pediu a Snape para matá-lo para poupar a ira de Draco, o Lorde das Trevas, ou uma alma mutilada por causa das tentativas de Draco de matar Dumbledore.

Mas não foi ele que pensou que o Lorde das Trevas mataria Draco pela varinha.

No entanto, apesar de Dumbledore ter pedido a Snape para matá-lo, não foi porque ele pensou que o Lorde das Trevas mataria Draco pela Varinha dos Anciões. Dumbledore pretendia que Snape conseguisse.

“He believes that the Elder Wand removes his last weakness and makes him truly invincible. Poor Severus …’

‘If you planned your death with Snape, you meant him to end up with the Elder Wand, didn’t you?’

‘I admit that was my intention,’ said Dumbledore, ‘but it did not work as I intended, did it?’

‘No,’ said Harry. ‘That bit didn’t work out.”
_{^{- Harry Potter and the Deathly Hallows, Chapter 35 (King’s Cross)}}

Ele provavelmente não esperava que Draco o desarmasse, então ele não achava que Draco estaria em perigo por ter sido considerado o mestre da Varinha Ancestral - ele achava que Snape o teria.

Sim, Dumbledore pediu que Snape o matasse para preservar Malfoy.

Como visto através das memórias de Snape no capítulo 33 de Relíquias da Morte :

Ultimately, of course, there is only one thing to be done if we are to save him from Lord Voldemort's wrath."

Snape raised his eyebrows and his tone was sardonic as he asked, "Are you intending to let him kill you?"

"Certainly not. *You must kill me."

E um pouco mais tarde:

"If you don't mind dying," said Snape roughly, "why not let Draco do it?"

"That boy's soul is not yet so damaged," said Dumbledore. "I would not have it ripped apart on my account.

Assim, vemos que Dumbledore estava preocupado que Voldemort mataria Malfoy, se Dumbledore não fosse morto, mas Dumbledore também queria proteger a alma de Malfoy. Ele conseguiu salvar a vida e a alma de Malfoy fazendo com que Snape o matasse.