If your goal is to improve your strength or lose weight, then do not fast anytime near your workout time (before or after) as this is the most important time for nutrients.
The saying, "Breakfast is the most important meal of the day," is not just a saying - it's a fact. The reason you need to break your fast before your workout is manyfold.
First, your body needs available ATP to perform the workout. If your body has no available ATP because you didn't eat for a long time before your workout, it will pull it from the quickest available resource, which is your muscles, not your fat.
Second, similar to the first point, is that your body makes the most efficient use of nutrients for recovery immediately following a workout. If there are no nutrients with which to deliver for recovery, your recovery process is sabotaged, restricting gains and limiting insulin spikes and protein synthesis.
Third, there may be nothing more damaging to metabolism than fasting. When you fast, your body is going into nutrient conservation mode and is more likely to put the nutrients you do consume into fat than to where you want them to go - your muscle. Metabolism is where real muscle gain and weight loss occur. Metabolism is responsible for natural protein synthesis, essential for muscle gains, and also sets the level of passive fat burning.
I think only you can answer the first part of your question on if it makes sense. In order for me to answer that, I'd need to know why you fast - religious purposes? Outside of religious purposes, fasting is not a good tool for most health goals.
IF you're going to fast anyway, and if your goal is either strength gains or weight loss, then you should time your fast furthest away from your workouts as possible, which for you looks to be the evening.