首先给你讲一下连词概念：
连词是一种虚词,用于连接单词、短语、从句或句子,在句子中不单独用作句子成分.连词按其性质可分为并列连词和从属连词.并列连词用于连接并列的单词、短语、从句或句子,如and,but,or,for等；从属连词主要引出名词性从句(主语从句、宾语从句、表语从句等)和状语从句(时间状语从句、条件状语从句、目的状语从句等),引出名词性从句的连词如that,whether等,引出状语从句的连词如when,because,since,if 等.
从属连词用非谓语情况比较少,这里我给你举几个并列连词用非谓语的例子
Tom was eating bananas when watching TV.
Jack is singing out there when being surrounded by lots of passers-by.
从上面两个例子可见,连词是可以接非谓语动词的.