SS and caloric deficit

The way I understand it, Starting Strength is not Starting Strength without a calorie surplus. Even so, does anyone have any experience doing the program for a period of time with a calorie deficit?

I'm currently 5'11 195 lbs with 22%ish bf. Did the first day of SS today with 170x5x3 squat, 185x5x3 bench, and 275x5x1 deadlift. I've also been jogging about 20 miles a week and eating ~2500 calories on running days for about a 700 cal deficit.

My main goal is to get my bf% down. I'd also like to drop to 175lbs as well, which is why I'm on a deficit. Increasing my lifts is a lower priority for now. That being said, will SS be completely useless if I work with a calorie deficit? Would it be a better strategy to eat more, increase my lifts, and just worry about getting the fat off later?