You will be severely limiting your strength gains. Note that I am talking about the amount of strength you will be able to gain, not just the rate of gaining strength.
In order to understand why, you have to understand a bit about General Adaptation Syndrome. Essentially, to disrupt homeostasis (the body's current happy place) to build strength you need to induce a certain amount of stress. That stress is in the style of strength training like Starting Strength. After that stress, you need to recover and during that time your body will super-compensate--making you stronger... Yay! Unfortunately, if you don't keep the regular frequency of the training, you won't be causing enough stress to force adaptation. Furthermore, the adaptation you are putting your body through with aerobics is working against the strength training (which is anaerobic). Essentially, what you do more of will win out.
I would start seriously considering the following questions:
- Why do I want to do Starting Strength (SS)?
- Why don't I want to lower the amount of aerobics I'm doing?
- What do I want from my training time?
- What trade-offs am I willing to make?
Also consider the fact you can continue gaining strength doing the SS protocol while you are doing aerobics. Of course, you will get to a point where the aerobics may cause you to stall a bit quicker because you don't have enough rest. A valid way to do balance the two is to add 20 minutes of aerobics after your SS workout.
But it's time to get honest with your goals and what you want to do. If aerobics is meeting all your needs, why do you even want to do SS? Essentially, all your training is a balancing act of priorities. At different times in your training one thing may have a higher priority than others, but that doesn't mean that they get completely cut out. If you want to emphasize strength, you'll probably have to de-emphasize aerobics.