In that I'm not a racer, I expect that I would have little to say regarding "training". Furthermore, "gear" is quite a broad category of what could hamper your training/riding. If what you are asking is "has the lack of cycle specific clothing caused you to not be able to train/ride?" Then, no it has not (for me). What cycle clothing does for me is help me regulate body temprature, while not restricting movement. The fabrics that they are made from are breathable, allowing for air to circulate as well as moisture wicking, which allows the sweat produced to be pulled away from your body. This helps to keep you dry and reduces chafing. These fabrics also are very elastic, which allows you to move freely and put your effort into moving the bike forward instead of fighting against restrictive clothing. I also need a decent sports bra, to prevent excessive movement in that one particular area (sorry guys). Add to that cycling shoes, which provide an interface to your pedals and have very stiff soles so that all of the power from your foot and leg goes into the pedal, instead of into flexing the foot. All of that goes to efficiency, which makes the ride better, but I cannot see the lack of it in any way preventing you from riding. Any other "gear" I can think of wouls be protective (from injury like a helmet, or from weather like a jacket) or informative (like a Heart Rate Monitor). I personally will not ride without a helmet, and I'm uncomfortable riding without gloves. My HRM is nice to have, but not a must.
What all of this boils down to is that in order to answer your question, we have to know what gear you are asking about.