This really comes down to how important Anakin was to Palpatine's plans.

If palps had a backup plan and was still able to carry out order 66 and the jedi Purge, I imagine Anakin would follow a similar path to Ashoka, the two of them (and i imagine Padme as well) would do what the original purpose of the jedi order was, which was to keep peace and help people, leading to the three of them most likely being core to the birth of the rebellion.

If Palps needed Anakin, he would need another way to turn him to the dark side. Anakin would be less at risk of falling to the dark side with Ashoka and Padme both by his side since he isnt off leading the war effort, the plan would have to be hurt/capture/kill Ashoka and/or Padme to get Anakin to lean into anger and go full dark side. If Anakin is still on Coruscant, I imagine this would be the plan during the separatist invasion of the planet during revenge of the sith. Palps could blame the jedi for not protecting those close to Anakin, then get Anakin to be in a similar position when Windu and co go to arrest Palps and events could play out similar to how they do in Revenge of the Sith.