I think it's possible. When I was weaker and had a lot more room for improvement, I believe the strength gain was associated to muscle gain while losing weight because I was able to handle the same workload that I normally do even while gaining (maybe I wasn't doing enough). It was no problem for my recovery. I did a bit of cardio to expend more calories to allow me to eat more while still being at around a 300-500 calorie deficit.
Now that I'm a bit stronger I feel like the strength gain is mainly because of increased lifting efficiency since I tend to lift with higher intensity and reduce caloric expenditure through cardio/conditioning as much as possible while losing weight. I have less room for recovery which makes me think my body is less likely to build muscle during that time.
With that said, I believe the amount of muscle gained while losing weight and not being very strong was minimal. IMO, having two separate training cycles focusing on fat loss while retaining strength for one and then focusing on muscle gain while increasing strength for the other has been a better approach. A comparison would be like me increasing strength by doing a lot of work, which can help increase my cardiovascular fitness as an added benefit. But is it really that important for me to measure and increase my cardiovascular fitness through indirect training? If it's not the primary goal, then it's fine to make progress in it but don't let the less important goals detract you from the primary one.