NeoPixel (or any other pixel type), can I split the data line at any point in the strip?

[DaveX]

You mean splice the datalines of two strips so the 3->4 ends are duplicates of each other? As in the #2 DO line hooks to the DI line on both #3s.

1 -> 2 -> 3 -> 4
      |
       -> 3 -> 4

Yes, that should work.

Adafruit_Support_Bill says so:

It is certainly possible to wire 2 or 3 in parallel. But 9 may be too much of a load on one pin. One thing that would probably work is to use Flora Neopixels as repeaters: Flora RGB Smart NeoPixel version 2 - Pack of 4 : ID 1260 : $7.95 : Adafruit Industries, Unique & fun DIY electronics and kits
Wire 3 of them to one pin. Then connect 3 of your strips to the output of each.

This too:

WS2812B LEDs question - parallel vs series

GreyArea: I've used the WS2812 LEDs quite a few times, but always in "series" (I think that's a misnomer as I believe they are actually connected in parallel on the strtip, but what I mean is I always have the LEDs sequentially, so the first LED that's connected to the data wire is LED0, then 1, then 2 etc). If they're on a manufactured "strip", they are, most likely, in series. Series means DOUT to DIN from one to the next. The power and ground are in parallel, but it's the data lines that …