No, if it had to be a tradeoff, I would not. I don't want to give up one for the other; I wouldn't feel complete as a person.
But I don't see that it has to be a tradeoff, really. I can keep/develop my intellectual abilities and also learn how to develop more emotional skills/awareness. I could in a sense use some my natural intelligence to help me develop/enhance EQ, too. It's not totally separate....there's overlap, intertwining.
Some of this EQ business is also tied into social intelligence/awareness/skills - those can be learned, at least on the surface; the deeper things, such as learning to be more aware of and read body language/emotional nuances, and respond more appropriately, would be harder to learn, perhaps, but possible.
Where I lack as far as EQ goes is not perception.....but what to DO with that perception, both within myself and in interactions with others. I'm learning, but it's sometimes a steep, rocky path, and I fall a lot.
I don't lack social skills/awareness, either, but I am just not polished, smooth, always gracious ......