Obviously cycling with club or others does help you improve your speed and distance. Notice that you have a will power to increase speed during the ride and eventually increase the distance for next couple of rides. Average speed for beginners are likely at 20km/h and medium experienced riders are at 24km/h. Ride in group will also show areas of your weakness that need improvement. A lot of skills you can get from the cycling group involve pedaling and shifting gears while ascending, when to stand and off saddle, how to get used with cadence, multiple use of your muscle, drafting etc.
Joining cycling club will get you motivated to maintain two to three rides a week which you are not able to do it alone as recreational rider and after a few rides you can judge your abilities whether to stay or to leave the club. Very often, there will be newcomers that have same abilities and even you can form a new club with them. Cycling is just so addictive that you will keep pushing your speed and gain more distance.
The downside, at the same time your credit card at risk to reach the ceiling limit because tendency upgrading is absolutely irresistible(actually got poisoned), you are not just sitting in the saddle and watch your friend upgrade to carbon frame or carbon saddle. Your attire will absolutely change from big short pants to tight short, from soccer jersey to racing team jersey (lycra) and absolutely your visit to local bike shop will be paid off once you have completed the event that you take part.
Example of carbon frame and saddle
Having said all that, Insyallah (without eating oily food etc) you will stay healthy and fit.