Strength Training

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I just went to my first Krav Maga class. It was awesome! I feel like I got a great workout. Lots of kicking and punching. I am still very sore in my upper body, and I did the class on Wendesday. My lower body is okay, but it was only my first class. During the warm-up we did some sumo sqats, push-ups and sit-ups. I would like to add some strength training to my workout schedule. I walk/job every day of the week except on Wednesday and Saturday when I will be doing Krav Maga. My question is: Is there any point to adding a strength training circuit to my routine once a week? I ask because I tend to get sore from strength training and I also seem to get sore from Krav Maga. There is a little strength training at the beginning of the Krav Maga class, and the whole workout seems to target specific muscles. I don't want to overdo it on the strength training. Plus, if I am sore from the strength training days then I will not be able to perform as well during Krav Maga class which I am paying a lot of money for (by my standards). I figured if I added one day a week on Monday that would give me enough time to recover before then after the classes. So, is there any point to strength training only one day a week? Will I still see any muscle building results? Will it be counter-productive in any way?