Sore quads alone won't affect your DL that much. However, squatting would affect it much more. You use your lower back and glutes a lot in both exercises, so if these muscles need recovery, you won't perform well.
No. I'm not thinking in terms of max/min. I'm thinking in terms of primary and secondary. As someone with your experience knows, there are many important synergists involved in both the sumo and conventional deadlift. Take one of these away, and no more deadlift. Fortunately, the OP doesn't have to take one of these away, he only has to deal with some DOMS and tightness(/possible weakness?) in his quadriceps.
Certain lifters, due to personal biomechanics and preferred lifting style will feel more stress on their anterior chain vs. posterior chain. Something that comes to mind is when a lifter doesn't "sit back" as much as "down", making the movement more like a squat. Trap bar deadlifts are another example of deadlifting with more of a quadricep contribution.
From experience, having sore quads affects my squat more negatively than it does my deadlift. I also have radically different experiences in terms of DOMS from my own workouts when I do squats vs. deadlifts. The OP will have to try and see, of course, but I did my best to make an educated guess.
Just hit a new raw dead PR tonight (460lbs) and my quads are pretty sore from mondays heavy squats. Soreness doesn't seem to affect my deadlift performance, i guess it depends on how sore you realy are.
AS it was said before your quads shouldn't be your primary mover.