Tl;DR: We are on target to hit one billion points
without Stark Foundation DonationsSo where are we now?

If we project linearly:

About 1.2 billion. But of course, that's cheating a bit, because that includes the Stark Foundation donation of 100,000,000 points, obvious in the chart. This makes it seem like our point earning is accelerating upward faster than it actually is. What if we remove that donation, and just look at the player activity alone?

A bit over 900 million points. But wait, weren't we projected to hit 800 million last week? Yes, we were. Here's last week's projection superimposed on this week's projection:

Our current projection is higher, because our average points per day is increasing significantly. We can see that in our points per day for the first two weeks:

This also removes the points donation. Our average points per day is rising. It bounces up and down, and most of those bounces are aligned with BG milestone reset days. On those days activity is higher, and on alternating days it tends to be lower. But the overall trend is upward. We can also see this, to a similar degree, in the estimated hourly activity:

We can see in particular we used to bounce above and below one million points per hour, and now we're almost always above that rate. The big spike in the middle is not the Stark donation, by the way. It is due to the fact that for a few hours the realm scoring mechanism stalled. That's why it dropped unusually low around hour 192 and then bounced up very high as it caught up. If you want to see what the Stark Foundation donation looks like:

Yeah, that's impossible to mistake for anything else.
Our average point earning rates have increased overall by about 30% over the two weeks of the event. We cannot necessarily assume they will continue to rise at that rate, but there is every reason to believe they will continue to rise as participation generally increases in the second half of the BG season. There are also still Elder Marks in locked milestones that will continue to fuel a lot of activity in the short term, and continued increases in GC population which will increase average point earning per match by some amount. Conservatively, though, if we continue at even reduced rates of point acceleration, we should easily hit one billion points scored
by the players by the end of the event. The Stark Foundation donations will just be gravy.
It is probably worth noting here why Kabam even decided to add those donations. They have a mountain of historical data I don't. They almost certainly could predict scoring better than I could, and almost certainly saw what these numbers would most likely look like. They appear to have selected one billion as a target we could and almost certainly would hit, and the additional milestones above as stretch goals for the circumstance where we did significantly more than predicted. So why add tons of points when they were not necessary?
The most logical reason is: sentiment. Left to our own devices, Kabam could predict our participation numbers would push us to one billion
if we did what we normally do during boosted seasons. But what if negative sentiment started to take hold, as it did with Crystal Cleanse? Then players could enter a downward spiral where they decide to hold back for fear of wasting effort in a losing cause, causing the numbers to fall short, causing more people to decide the whole effort was doomed to fail. The points injections eliminate that possibility, or at least neutralize it. If players believe that getting to at least one billion is almost inevitable, then they are less likely to fall victim to negative sentiment.
This has some pros and cons. In the short term, it mitigates negative downward spirals. But it can also create a sense of entitlement, that players will think they deserve all the realm rewards no matter what they do, and thus there's no need to actually do anything. That's something to watch out for in future realm events.
Even I originally estimated our point earning potential incorrectly, for a number of reasons: underestimating historical participation rates for one, and not accounting for the large influx of elder marks in the realm milestones for another. But careful analysis of the data shows that the trend is our friend in Battlegrounds Blitz. If we fail to reach one billion points
on our own it will be because the game experiences a week of downtime or something. Otherwise, we're on track to get there.