In short NO.
In a bit longer. The pulley lining is fixed into the cill by means sitting in a slot cut in the cill, similarly the inner and outer cheek are cut into it front and back.
If you cut the cill out between the pulley linings and replace it with a square ended bit of timber it WILL fail, always. This is known as "slipping" a cill.
You should replace the entire cill.
You will lose all the structural integrity of the box, nothing to stop the two sides wandering about.
Cut out the pulley lining above the pockets, cut out the rotten bit of outer cheek either side you can leave the inner cheek in there but cut through all nails with recip saw, cut the cill in the middle and pull the centre out (do not forget the window board will be nailed to it so cut those nails too ).
Replicate all the timber you removed and put it all back using a decent epoxy (timbabuild or windowcare etc), the cill will fit once you have cut the ends for the inner and outer cheek (twist it in) then assemble all the other bits.
Note I have assumed a proper box sash window, with weights and pulleys if its a spiral balance window it won`t be made like this.
Ollie