Yes, you can run unattached in many meets. Some meets directors will not allow it though. Something you should consider as well is travel. If you live in the Mountain West (or midwest to a lesser extent), most meets are several hours away or more, and none are very big, which may or may not be a problem depending on how fast you are. If you live in California or the East Coast, this won't be a problem though.
I've done both. There are pros and cons to both. It depends on the program and those involved with it. There are some coaches and programs out there which are just nightmares, and you'd be much better off running on your own (unless you would be on scholarship and need to the money). There are also programs out there which are great and great to be a part of. Either way, when you're a part of a team, you sacrifice a lot of freedom. You gain friends, gear, travel, medical care, etc, so it can be worth it. Most on here would probably say it is worth it. Again, it depends on your situation and the program/people involved.
My advice is the opposite of what you're considering though. I suggest joining the team right away and seeing how you like it. Give it a year as the first few months can be a bit rocky. If you don't like it after a year, quit and run on your own. It will be hard to get to know the coach and team very much if you're running on your own, especially if you aren't spitting out steller times.