I'll just answer this to get it off the unanswered list.
This isn't going to happen, and there are a few strong reasons why this would be the case.
First off, the chat can't really be compared to something such as upvoting or downvoting in terms of privileges. While these are ancillary to the PokeBase experience, the chat is one of the primary sections of the Pokebase. For a comparison, to have a point block placed on the chat would be like having a point block placed on the PokeBase, Meta, or Battle Subway.
The chat's primary purpose in relation to Pokemon is to facilitate trades and organize battles. New users do not have the connections on the site in order to organize such things over g-mail. Block the chat with a point requirement, and the rest of the site will be filled to the brim with such requests.
Another purpose of leaving the chat free is that it allows people to communicate with other users in order to learn about the site and how it functions. If a person is unsure of the rules or such, and are of a younger age where they have trouble figuring things out for themselves in this regard, the chat is a great place for people to go. We don't want even more repeat meta questions for such things.
As mentioned in the comments, there are a significant amount of people who use the chat without posting on the site. A large amount of these people are fine and upstanding users. It would be rather unfair of us to just basically kick them out of chat.
It's likely this would also lead to an increase in spam upvoting, as users would ask easy to answer questions that require little more than saying "Yes, Charmander can learn Flamethrower" and then have other people sympathetic to them upvote such a question in order to allow them to use the chat.
The idea of people being able to go on Showdown to chat is also very flawed. First of all, that would just be shifting any problems on this site over to the Showdown server. Second, Pokemaster does not gain ad revenue from the Showdown server. He does from the chat though. I'd rather Pokemaster gets money rather than some Smogonite who never did a damn thing for anybody here on the Database.
Spammers and trolls are a problem on all sites, yet going to such extreme measures to stop them will only lead to a reduction in the enjoyment of the site for others. Even those with points will be affected by it, as it will likely lead to a decrease in new blood that actually sticks with the site for any extended period of time, as well as drive off users who are currently using the site. Let the mods and editors deal with spammers and trolls. We already do a fantastic job at dealing with them, and we do it without restricting those users who aren't trolls.