Q:

How important is understanding Software Project Management for an indie?

I ask this because I'm curious to know from people who actually support themselves by making games, if their project management skills contribute to determining the success of a project?
I also have this feeling for some reason that having too much project management can strangle the creative process. Maybe there is a way to prevent that from happening. I don't know. 
Thanks to all that reply.

A:

Sometimes "strangling the creative process is necessary", if the creative process is so out of control that it's preventing you from shipping a game.
PM (project management) is one of those things that, if things are going smoothly, you hardly notice that it's there.  It's primary goal is to keep the team focused on what the real goal is.
Some things in the PM toolbox can actually help the creative process.  The idea of short sprints to a "shippable product" can put you in the quick iteration mindset.  Daily standups are useful as a communication tool.  But it's all about how you apply it and where.
The relative importance of PM depends on the project and the team.  Sometimes it doesn't add anything.  Sometimes it's the difference between success and failure.  

A:

Caveat and summary - I'm basing my answer on the idea that you have a good team to start with.  A good team doesn't need a project manager, but can work together towards a common goal as a team.  "Bad" teams (or really complex projects) need a project manager.
There's an old joke in the modding world of the guy who posts on some forum that he has an awesome game idea, and he just needs a coder, a modeller, a skinner, a sound guy and a level designer.  And what's he going to do?  He's the "leader" or the "idea guy".  The point being, the poster doesn't have much to offer, and really needs to be part of the development team.   
Don't let your desire to add project management to a game turn your project into one of these.  Indie implies small team, and small team implies very flat organizational structure.  And that implies that your team can work independently towards a common goal that they all share and understand.  
Some teams need no management and are self managing - a team of equals who's synergistic efforts combine into something good.  This is true when the developers are working towards a common shared vision and goal.  
If that vision is not shared, then there needs to be something that guides everyone towards the same goal.  That can be a project manager, but it just as easily can be a good design document that everyone follows.

