No, Zephyr isn’t like that at all. Neither is Flash Sentry, despite the number of people who have reacted to him as though he is.
I actually think he has some depth to him. In fact in many ways he reminds me of Rainbow Dash. He, like she, is always trying to appear cool; always trying to sell himself as better than the average pony (Dash, of course, gets a pass because she actually is as awesome as she claims to be, but I digress). Yet underneath they both have an intense fear of failure and often suffer from self doubt, which in turns leads them to do stupid things (giving up for Zephyr, pushing herself harder and causing more mistakes for Dash).