Yes, if you can find a group who are better than you and are willing to give you advice and encouragement you will improve quicker than any other way.
As well as getting fitter you need to learn all the skills of riding in a bunch. There are a lot of fit cyclists who are lacking in this department, which is a shame for the individual as riding in tight formation will help make you a better rider and at the same time stop you being a nuisance to others.
Learning to pedal fast is good.If you learn to spin early on you will benefit when you start to push bigger gears. this should all come naturally when riding in a group. Many years ago I was struggling on club runs to keep up, an experienced ex international told me bluntly, "You have a lovely pedaling style but you are pedaling elegantly out the back, sometimes you have to just push hard". Obvious maybe but I needed to be told.
Even if you cant find a helpful group you will still benefit by using them to set yourself both skills & fitness targets, like how long you can keep up with them on climbs, closing gaps, riding on a wheel, through and off etc and learning the etiquette of bunch riding.
As a start, try & add some miles to your commute, make it interesting by doing intervals. Also find a circuit of a couple of miles with a short steep hill on it. After a good warm up ride try to ride up it in the saddle so you reach exhaustion just as you reach the top. recover over the circuit and repeat. Try 3 to start and then ride home. when you see improvement increase the number of laps