In your scenario with the one sarge on A1 and the general on B2, I'm assuming move one for the auto draw is the very next move. How it goes kind of depends on whose move it is. If the general has not chased yet in this situation and it is his move, then the sarge's win handily because they already have the Two Squares advantage. The general can only chase 10 moves. Say he chases to B1 and our A1 sarge (#1) goes to A2. The general proceeds to chase in the 2nd file all the way to the other side where the sarge ends at A10. The general will be stopped from moving to B10 by HmmNess and will therefore retreat to C9. He now does not have any Two Squares advantage over anything. Then our intrepid A10 sarge #1 will step up to B10, and an invariable end commences for the general. He chases three times and ends up on C10 with the first sarge now at B9 and then the general is forced to move to D10 next, and again our B9 sarge moves into C9. After another three move series, the general is at D9 and our sergeant #1 is at C10. Now the general has to move to E9 in front of his non-movable piece (bomb or flag) while our intelligent sergeant remains at C10. Instead, partner sarge #2 waiting at J1 moves to J2. The general has made 18 moves at this point. He moves back to D9. Sarge #2 moves to J3. The general chases to D10/D9/D10 again. The first sarge is now at C9. The general chases three times C10/D10/C10, while the sarge evades D9/C9/D9. The general chases again C9/C10/C9 while the sarge moves from D10/D9/D10. The general has now moved 28 times. Now HmmNess will preclude him from moving to D9 and chasing a tenth move in a row. The general moves to C8. Sarge #1 is at D10 next to a non-movable. Sarge #2 moves to J4. The general moves to C9. Sarge #2 moves to J5. The general resumes chasing around the 2x2 set of squares from D9/C9/D9, then to D10/D9/D10 then to C10/D10/C10. Sarge #1 is at D9 and the general has moved 39 times. The general must now move away again, due to HmmNess, to B10. Sarge #2 moves to J6. The gen moves back to C10. Sarge #2 moves to J7. Now the general strikes up chasing again. D10/C10/D10; D9/D10/D9; C9/D9/C9. Sarge #1 is now at D10 again, and the general has made 50 moves. The general moves away to C8. Sarge #2 moves to J8. Gen to C9. Sarge #2 to J9.
And it all repeats. The gen chases his set from D9/C9/D9 to D10/D9/D10 to C10/D10/C10 and sarge #1 ends up on D9 again. The general has moved 61 times. He is forced to move away to B10. Sarge #2 to J10. Gen moves back to C10. Sarge #2 to I10. The general chases D10/C10/D10; D9/D10/D9; C9/D9/C9 once more and sarge #1 is at D10 now. General to C8. Sarge #2 to H10. General back to C9. Sarge #2 to G10. The general has now made 74 moves. Sarge #1 dies valiantly on the E10 bomb. General makes 75th move to D9. Sarge #2 wins the flag at F10.
That's one way it could go down anyway. Whew!
This would be complicated to show even using the Stratego Editor.