Is it possible to run simulation with stability on Accelerator?

Yes, Accelerator can run simulation with preserved temperature settings that you set in the desktop version.

It is possible to do stability simulation on Accelerator. Unfortunately the Web GUI does not show the temperature settings yet, but the settings you set in the Desktop will be preserved after you upload to Accelerator.
In a future version we will show the temperature settings, so you can change them in the Web GUI as well.
 
Edit
The stability option, only using Monin-Obukhov length, is now added to Accelerator and can be  selected in Wind Fields