In theory, an invite system sounds good for a smaller company in its infancy.
They know exactly how many people want their phone and they can make to order, reducing manufacturing costs as they don't have to make a ton of phones and thus, don't have to risk having a warehouse full of unsold devices (like the Galaxy S5). It also provides an orderly method like a queue, basically a "first come, first serve" method, where the first to come is the first to be served, unless that person may have made a reservation. It's not as good as buying a phone outright in the conventional way, but in theory, an invite should make things orderly.
Sadly, the way OnePlus has handled it is nothing like how I mentioned. You basically get a spot, but you're not guaranteed that spot. So let's say you're in a pool of 100,000 guys and you're in spot #1500. You've got that early spot and everyone else is late. One day later, you're at spot #15,000, because some guys behind you managed to spam referral links in other places. The next day, you're at spot #50,000.
I personally think that the whole referral system is making this whole invite system pretty messy and I would personally either buy an invite off someone or the phone itself off Swappa (might be used). Personally, it's not worth my time to be sitting in front of a computer and keep sending referral links to maintain my place in the queue. I've got better things to do than that and I'm personally not that desperate to get a $389 phone, especially when there are other similar offerings out there like the Moto X 2015.