No.这个句子出现了两个谓语动词——go和take,这是英语语法所不允许的.可以改成：
We go to the park by taxi,OK?
We go to the park in a taxi,OK?
We take a taxi to the park,OK?
Let's go to the park by taxi,shall we?
Let's go to the park in a taxi,shall we?
Let's take a taxi to the park,shall we?