To an extent. But Obi would always put up a better fight against Anakin than Dooku having 1)instructed him and 2)having mastered the form best suited to tackle him
Though I agree Obi-Wan would lose to Anakin at the beginning of ROTS. But I also doubt Dooku would beat Anakin on Mustafa.
I think Dooku could win that duel if Anakin was in the same emotional state as he was when fighting Obi-Wan. Obi-Wan stalemated him in a Force contest, so Dooku should be able to beat him with the Force.
That said in all of their fights in TCW, Dooku did push Anakin around quite a bit with the Force, but never anything decisive enough to give him the win. And I doubt Mustafa Anakin was < TCW S4 Anakin. Certainly not < TCW Movie Anakin.
So just seems either due to physicality or good natural force defences, that Anakin can take Dookus Force attacks better than Obi-Wan.
Dont get me wrong, would likely be a good fight, but I think in the end stamina would be Dookus downfall.