I don't think that working at gojet will stop you from getting to a major (many gojet pilots will make it). But It can hurt you, I personally know one ex-pilot who is a recruiter at a major airline who has destroyed resumes from gojets and freedom pilots! He is only one of many people who might receive your resume, if someone else gets it you might be OK. But it is a risk! If you work for gojet at some point someone will try to make your life harder.
Don't get me wrong. Working at gojet is not a death sentence, but it may slow you career progression rather than jumpstart it.