Definitely sounds like you may have missed the prime conversion temps. But back to your original question on sparging techniques, I've noticed that Beersmith does have a box to check on whether or not the first runnings are drained before sparging begins, so at least someone at some point must have sparged without draining the first runnings. I could see if you were mashing really thick (or using a bunch of wheat/rye) and wanted to make sure that the mash was fairly loose before draining, you could add your sparge water without draining. I'd just aim for hot enough water to bring everything up to about 165 or so and stir it really well if you wanted to do it that way. However, I think most people tend to drain off the first runnings, then add back the sparge water hot enough to bring the grain-bed temp up to about 165, stir real well, then drain the sparge.
The benefit of draining the first runnings is that you wind up extracting more sugars than not draining. Take the two examples. Your grain bed will hold a certain volume of water no matter what way you sparge. If you add the sparge water without draining the first runnings, you wind up with a mash that is at your pre-boil gravity (let's say about 1.04). So after draining, your grain has held onto wort that is at 1.04. If you drain the first runnings, you remove a good deal of the sugars in those runnings (let's say a gravity of 1.07). Your grain will then hold onto some wort at 1.07, but when you add the sparge water, it dilutes that wort, as well as potentially washing a little more out of the grain bed. Your sparge winds up being lower than your total gravity (1.03), so after draining your sparge your grain bed is holding wort that's only 1.03, instead of 1.04 without draining the first runnings.