This depends on what the team is like and what the project is like. If we are talking about a large system that is being developed and maintained by a team of developers, then the answer is "probably not". In such a case, regardless of who wrote the original feature, the team as a whole has to maintain it. This means that as much as possible, each feature should be developed in a way that any other member of the team can jump into the code at any time. If your the only guy who knows F#, that's not going to work.
A manager also has to be concerned about hiring new developers. Can they find new F# guys off the street? I know this attitude make it hard for newer (and possibly better) languages from taking hold, but at the end of the day, our job is to deliver working software, not to promote good languages.
On the other hand, if the entire team knows F#, or wants to learn F#, then maybe it's ok. Regardless, it needs to be a team decision, as does everything else that goes into the project.
On the other hand, if this something completely separate from the main task, then maybe it's ok. A few years ago, we had a task to write a program to do some back-end database manipulation to create data for our client application. The dev wanted to use Perl, and since it was entirely decoupled from our client (which used C++) and since it isn't hard to find Perl people in the group, this was no problem.
Ask yourself what would happen if your dev got hit by a bus half way through development? Will it be a problem that his code is all F#? That should answer your question for you.