I have an external microcontroller programmer. Could I possible just purchase an ATmega128, upload the Arduino bootloader, and write a sketch to it without an Arduino board?
You can, but make sure you get the 168, not the 128. They're a bit different, the Arduino IDE doesn't support the 128 without extra work.
Just make sure you get a resonator, or a crystal and some caps. And of course, a pullup resistor for the reset button! (and a button if you don't have some)
You can actually buy some 328s with the Arduino bootloader already on, comes with a 5v regulator, 16mhz resonator and a socket for soldering the chip without hurting it. All for $7!! Free shipping to US and Canada. I've bought two from the guy, they're on eBay.
http://search.ebay.com/_W0QQsassZkylej1050QQhtZ-1
Sorry for the rambling.. but it's a good deal if you're buying chips.
Short answer to your quest, yes, but make sure you get the 168, not the 128! 
Can. Specifically to support the chip mega128 a module / plug-in for shell Arduino. Initially, all done in the project Wiring. But there is a slightly different internal architecture of the kernel (the core of the pulsing time of quartz). And (not always) incompatible libraries with Arduino.
http://marshal-lab.ru/node/11 # ENG
Also, there are circuit and PCB layout for mega128.
Ah, yes. Two versions of the core clock: Timer0 and Timer2 - choose any.
With Ardino everything is possible 
Are these kits no longer for sale? I cannot find them on his page anymore.
He doesn't seem to sell them anymore :(. I keep hoping he'll list some more soon :-/..
What are you trying to do? Do you have your eyes on an existing 128-based board that you want to use with the arduino libs? Or are you looking at a 128 because you need the extra flash/ram/io? Have you looked at getting an Arduino mega? It's 1280 based which is essentially a 128 with some extra I/O and twice the ram (8kB).
Differences between the 128 and the 1280 aren't that great. Since the Arduino software already supports the 1280 porting the libs to the 128 shouldn't be too much work. Have a look at the appropriate datasheets and avrgcc header files. Mostly it's a matter of adding some #ifdefs and filling in the proper registers.