The short answer is, "Yes - but it depends".
You can always "go public" if you want, but if you really want to enjoy your BL experience then you should get together a fixed/known group of friends. Some questions to help you organise a co-op group:
- In what time zone are you located (ie., are you looking for EU/NA co-op players or AU/NZ)?
- Do you just have the base game or do you have any of the three DLCs (affects who can host, where you can travel on Pandora, etc)?
- On what platform are you playing (PS3, XBox360 or PC)?
- If PC, do you have Borderlands from Steam, retail or some other method (ie., would using Steam to co-ordinate with other players be an issue for you or do you prefer Xfire or something else)?
- If PC, do you have an external voice app (TeakSpeak, Ventrilo or Mumble) that you use with other TOG divisions (because in-game voice for Borderlands isn't generally worth the effort)?
- What up/down speed is your broadband connection (again, relates to who can host)?
Sorry there's a bunch of questions there, but most of these generally come up when trying to sort out co-op groups so it's easiest to just get 'em out of the way at the outset.