You can see instantaneous and averaged power, among other calculations, using a head unit or a mobile app like Wahoo Fitness, just like you can with any other bike sensor.

Unless you are already very strong on the bike, knowing your power profile and using it to inform your training will increase your speed a lot more than a new wheelset. It takes commitment and doesn't come easily, so it's not for everyone. If your heart says you'll enjoy slick new wheels and be more motivated to ride, then you may be better off with those.