是的，两者有时是可互换使用的。如：

Asked / Having been asked to stay, I couldn’t very well leave. 我被邀请留下，遂不便离开。

但是注意，虽然两者都表示被动和完成，但 having been done 还强调完成，但 done 则并不一定强调完成。如下面的句子并不强调完成，所以不宜用完成式：

Wounded in action, he was twice mentioned in dispatches. 因为在作战中受伤，他曾两次在战报中受到表扬。

Shocked by the results of the elections, they now want to challenge the validity of the vote. 选举结果令他们很震惊，他们现在要对选举的可信性提出质疑。