How much of an aerobic training effect you get from your gym weight lifting sessions depends on your fitness level. If you are fairly unfit then any stimulus to the aerobic system will be positive. A well trained endurance athlete will get much less benefit to his sport (unless it is gym weight lifting) from this type of training. This accounts for the hype surrounding the fitness fads of high intensity interval training done in a gym setting using weights. They are sold to an unsuspecting public as accomplishing the same thing as basic, tradition long duration low intensity workouts but in much less time. THEY DON’T.
What you are doing is called Muscular Endurance training which has been a staple of endurance training for decades. But it is used in conjunction with and as a supplement to, long duration low to moderate intensity aerobic base training……Not as a replacement for this base training.
You can see gains for sure this way. One way to tell how much aerobic benefit it is having is to do a time trial at the start of such a program of HIIT and then repeat the TT 8-12 weeks later. If you see a gain in performance then you have your answer. Chances are good you will see a gain over the short term. However you will never maximize your endurance potential longer term with this approach. We have written a book about this this called Training for the New Alpinism and you might want to read the physiology chapter. You also might want to watch this video lecture I did last November. https://www.facebook.com/uphillathlete/videos/1207164636050638/
I hope this helps.