What happens to a RAID 0 array if some of the constituent drives are unavailable?

If you use actual RAID 0 (striping without redundancy), then if any one of the drives fail, is disconnected, etc., the entire array fails. You won't be able to access any of your data in such a scenario. The OS is unlikely to recognize the remaining drives as having an identifiable file system; I don't know exactly how OS X handles that scenario, and it probably depends on what you've put on the array too, but that's largely irrelevant at that point.

It might be possible to recover some of your data (the data which happened to be stored on the still-functional drive), but even that depends very much on the specifics of the RAID implementation and those of the data.

That is why, except for specialized purposes, RAID 0 is often a very bad idea. It mainly gives you speed gains, but it comes at a relatively high cost in terms of risk of loss of data. Usually, one does RAID 1+0 (mirroring, then striping) or perhaps 0+1 (striping, then mirroring) rather than pure RAID 0. Pure RAID 0 is mainly useful for transient data where speed versus cost is the most important consideration (and in such situations, fast SSDs have for all intents and purposes totally outcompeted fast rotational drives).

Also note that depending on the software (even if it's in firmware), it might not be trivial to grow even a RAID 0 array after it has been created.

Just how much data are you dealing with, and what alternatives are available to you? For example, might four large drives in a RAID 5 (striping with single parity) configuration be practical? Four 2 TB drives in RAID 5 will give you 6 TB usable storage space and although you'd want to replace a failed drive as soon as possible will survive the loss of any one drive with no immediate harm to the data. If you have a full backup to elsewhere and can live with the downtime needed to restore from backup if a second drive fails before you have had a chance to rebuild (resilver) the array, I think you'd be okay with single parity. If you're paranoid, go for double parity, but it'll cost you another drive's worth of storage capacity.

It also sounds like what you are really after isn't so much RAID as it is a practical approach to volume management, so that you can grow your storage solution as your needs change. If that's so, you may actually want to have a look at ZFS, which is in essence a combined volume manager and enterprise-grade file system that allows you to relatively easily grow your storage solution piecemeal. It might not be a practical solution for your system disk, but for your data storage needs it just might be what you are looking for. If this is what you are actually after, I would strongly suggest posting that as a question, as it really is only peripherally related to RAID.

And of course, the obligatory comment on the subject: regardless of level, RAID is not a backup.