Excitement deprived me of all power of utterance ,in which case I would but stand there, nodding and waving.

你的理解基本正确。我转换一下你就清楚了。

Excitement deprived me of all power of utterance ,and in that case I would but stand there, nodding and waving.

这是并列句，由and连接。in that case指“在这种情况下”，that为指示代词，指代前句的内容。

并列句的两个分句都是说话人想要强调的。如果说话人像突出第一个分句，第二分句就成了次要信息，只要去掉and，将指示代词换成关系代词，第二分句就成了从属分句（定语从句）：

Excitement deprived me of all power of utterance ,in which case I would but stand there, nodding and waving.

非限制性定语从句一般都是这么来的。