He thought a new road was being built and that it would be f

不可以去掉,当出现多个宾语从句时,只有第一个that可以省略,其余的不省略.本句的意思是：他觉得一条新路正在建设中,而且将很快竣工.
再如：He told me that (可省)he was a teacher and that（不可省） he had taught for ten years.
我是老师,一定正确的,