Yes it is OK to do cross races (or any other races) without a team. Cross is a bit easier as it is less of a team event than a road race, but any racing is possible without HAVING to join a team. On the other hand having the support of a team, and the expertise of your more experienced teammates can make the whole thing easier and more enjoyable.
How teams recruit is really up to the indvidual teams. The team I am on works mainly on taking on beginners - even if you've never raced and may not even be totally fit, as long as you are willing to try we are willing to teach you. Other teams are more interested serious development and will hand select riders that they think will do well.
Now is generally the time to start looking to talk to teams. All of the teams in this area use the fall to recruit new members - we usually close our roster some time in November. To find teams in your area your LBS (local bike shop) is usually a good place to start, but look around on the internet too. If your state has a bicycle association you will usually find links to local team's websites too.
Good luck and have fun in your cross races!