I don't believe it's possible to have creativity without emotions, and I've got citations to that point (which are apparently quite controversial, that comment has been fluctuating heavily in score) [1].
It's possible to put constraints on your emotions and to not immediately do something because you feel like doing it. This is the essence of emotional intelligence, and of maturity. The thing is that this is a conscious process: you are expending your limited attention on watching your behavior and ensuring it conforms to the desired norms. (If you internalize those norms such that conformance is unconscious - well, then you've internalized the existing norms, but the point of creativity is that you're trying to break out of those unconsciously-internalized customs.) That means you're not expending that attention on the details of the problem itself. Most of the problems involved in revolutionizing an industry with computer code are immensely complex and require all the attention you can give them.
It speaks directly to the nature of creativity. Is creativity simply the discovery of the new; or is it an expression of desire for the new? Is it something else?
Hmm...
Although, to the original concern: I don't believe constraints on behaviour necessarily constrain emotions; such constraints influence emotions, but I wouldn't expect a general suppression of emotion.
It's absolutely a false dichotomy to assert that there can either be creativity or there can be constraints.
As a game developer, I look no further than the numerous game jams with artificial constraints as evidence that creativity can flourish within the confines of constraints. One might even argue that creativity is given constructive direction by way of constraints.