Will fasteners straighten a pressure treated bottom plate?
Sometimes you can get away with this. However depending on how bad the lumber has warped, sometimes you can't.  You will know when you can't when in the process the lumber splits and breaks.  Also you will incur additional labor and hardware costs.  The overall quality of the job can be affected by sub-standard lumber.
Note to self: Always when purchasing new lumber, lay flat and stack to avoid warping.  If you know it will be awhile before you can get to it, you can weight your stacks. Additionally, try to keep the lumber from drying out before it is framed into place.