Is It Normal for a Post to Show at the Bottom of a Tooth?

It depends what you are calling the bottom of the tooth?? It would be much easier to tell what you are talking about if you enclosed a picture. What you may be calling the bottom, someone else may call the top??? If you are talking about the biting surface, then you maybe be able to see the post or possibly feel the post. You need to remember this is a temporary phase, and you should not wait too long to get the crown on the tooth. I have seen many teeth fracture beyond repair when no crown was placed after a period of time. 

Typically, when a tooth gets a post it is because there was significant loss of walls or tooth structure. The post is cemented into the root and a build-up filling material is placed around that post to engage and hold the material in. The post should have been cut to a length just short of the top of the tooth (chewing surface) so that when the filling material is put in, the top of the post is burried under the filling and not visible. It can still be ground down flush with the filling so that you don't feel it with the tongue.

I would recommend to get the crown sooner rather than later. Once a post if placed, the tooth is more prone to fracturing in a way that may not be saved. The crown will reduce the chances of fracture.  

Good luck

Dr.T