The commercial advertisement is one of the things that we ha

可以,把它去掉以后就变成了状语从句的省略.类似的列子还有很多,
when doing homework=when sb+be doing homewrok,
when coming to school=when you come to school等等
补充一点省略的知识：省略的时候是从句里的主语和谓语一起省略,而不是只省略主语或者只省略谓语,你给的例句中的we are就是主谓语一起省略的情况、.