É improvável - o Ministério estava efetivamente em guerra com Dumbledore.

A Ordem da Fênix é uma sociedade secreta fundada e liderada por Dumbledore - era claramente sua.

“Is anyone going to bother telling me what the Order of the Phoenix –?’

‘It’s a secret society,’ said Hermione quickly. ‘Dumbledore’s in charge, he founded it. It’s the people who fought against You-Know-Who last time.”
_{^{- Harry Potter and the Order of the Phoenix, Chapter 4 (Number Twelve, Grimmauld Place)}}

No momento em que Harry foi resgatado dos Dursley, Dumbledore e o Ministério estavam em guerra. Fudge disse que qualquer funcionário do Ministério não deveria estar em contato com Dumbledore, ou eles seriam demitidos.

“Well, apparently Fudge has been storming round the Ministry checking that nobody’s having any contact with Dumbledore,’ said George.

‘Dumbledore’s name is mud with the Ministry these days, see,’ said Fred. ‘They all think he’s just making trouble saying You-Know-Who’s back.’

‘Dad says Fudge has made it clear that anyone who’s in league with Dumbledore can clear out their desks,’ said George.”
_{^{- Harry Potter and the Order of the Phoenix, Chapter 4 (Number Twelve, Grimmauld Place)}}

O Ministério queria tanto Dumbledore quanto Harry desacreditados, já que Fudge estava tentando negar que o Lorde das Trevas havia retornado porque ele não queria enfrentar essa possibilidade.

“How can he think that?’ said Harry angrily. ‘How can he think Dumbledore would just make it all up – that I’d make it all up?’

‘Because accepting that Voldemort’s back would mean trouble like the Ministry hasn’t had to cope with for nearly fourteen years,’ said Sirius bitterly. ‘Fudge just can’t bring himself to face it. It’s so much more comfortable to convince himself Dumbledore’s lying to destabilise him.”
_{^{- Harry Potter and the Order of the Phoenix, Chapter 5 (The Order of the Phoenix)}}

Fudge não era a favor de Harry - ele estava feliz por ter uma oportunidade de expulsá-lo.

“What Cornelius doesn’t know won’t hurt him,’ said Umbridge, who was now panting slightly as she pointed her wand at different parts of Harry’s body in turn, apparently trying to decide where it would hurt most. ‘He never knew I ordered Dementors to go after Potter last summer, but he was delighted to be given the chance to expel him, all the same.”
_{^{- Harry Potter and the Order of the Phoenix, Chapter 32 (Out of the Fire)}}

Então, o Ministério quase certamente não aprovou a missão de recuperar Harry dos Dursleys.

Parece bem claro que eles não foram autorizados

Quando Harry pergunta ao Advance Guard como eles estarão viajando, ele recebe a seguinte resposta:

"Brooms," said Lupin. "Only way. You're too young to Apparate, they'll be watching the Floo Network, and it's more than our life's worth to set up an unauthorized Portkey.

Se o Ministério tivesse autorizado a recuperação, eles poderiam facilmente ter autorizado uma Chave de Portal também. Além disso, não haveria medo de usar a Rede de Flu - quem se importaria se o Ministério a assistisse se o próprio Ministério autorizasse a recuperação?