非谓语动词后面可以跟句子构成宾语从句吗?

当然可以啊,宾语从句的语法功能和名词是一样的,可以把它看成是名词性成分.
比如：
Not knowing what he should do,he began to cry.这里就是分词短语作状语的情况下,在非谓语动词后跟宾语从句what he should do
To understand what the teacher was saying,the students listened carefully.这是不定式短语作目的状语,what the teacher was saying 是宾语从句