I agree. Progress is subjective though, if you mean progress in terms of technology and material advancement, then yes, based on logic alone we will be able to do so. However, if progress is to be evaluated on a whole, then emotions would definitely need to play a part.
Living a life without emotions might be possible, yet pointless, don't you think? Of course, the only people who would realise the pointlessness of living without emotions are the people who actually do have emotions. Luckily the emotionless won't consider suicide or ending life, though, just based on the fact that, well, they don't care.