You will still have the same resolution, just spread over a larger scale.
Think about it. Resolution = the number of counts that you have to work with
The thermocouple reads directly in degrees with one implied decimal point. You take and multiply that number by 10. It's still the same resolution. You multiply by 1000, it's still the same resolution. You divide by 1000, it's still the same resolution. You haven't changed anything except the decimal places. The counts are still the same.
So your thermocouple is 32.0 degrees (300 counts) to 1300.0 degrees (13000 counts). That is 12680 counts (or steps if you want to think of it that way) You can reduce the number of counts by doing integer math, but you can't get more counts by multiplying.
32.0*2 to 1300.0*2 still has 12680 counts (or steps). You have just increased the number spread by a factor of 2.
(32.0*1000 to 1300.0*1000)/4095 still has 12680 counts (or steps). You have increased the number spread between counts (or steps), but you haven't increased resolution.
All you have changed is the count of numbers between each step. You haven't added any additional counts.
Now if a larger number scale will improve math resolution, then you have something. But since PID is already doing Floating Point, I sincerely doubt this helps much.