This sentence can be understood easily by Chinese,but I don't think it's correct grammatically.

I agree with 阿馨。 Actually, this sentence is corret grammatically, and it can be understood easily. But, it sounds a little wierd. We usually say "我是个很守时的人。"

”我是这么准时的人“ is absolutely correct from the view of grammar. But what's more important, I think, is you can feel the mood of who says "我是这么准时的人“。 Maybe he or she has been waiting friend for one hour, so he ore she emphasize this, expressing his upset.

我是这么准时的人。绝对正确，没任何问题，一定要完善的话可以说成： 我就是这么准时的人。 这句和“我是一个准时的人”，“我是一个很准时的人”，相信母语都能分辨它们的区别吧。多个“就”，少个“就”不影响整个句子的正确性和基本含义。 比如 你会是这么准时的人吗？ 当然，我就是这么准时的人。

我是一个很准时的人