Will be arriving in Prague in Sept., on a Wednesday and taking NT to Warsaw on Monday night; then taking NT from Warsaw to Vienna on Friday night. Right now I plan on purchasing our tickets for the NTs on the day we arrive in Prague and Warsaw. Is this enough in advance?
I'm not worried about places selling out before then, assuming you're a bit flexible in what you'll take. But I'd try to buy both tickets in Prague, for convenience.
I thought sleeping accommodarions sometimes sold out?? Perhaps not in that part of Europe, and I know they're in less demand due to the advent of budget flights. But still, if I was not willing to buy a last-minute airline ticket and could not sleep sitting up, I'd take no chances. It's not as if there are lots of options. There's usually just one optimum departure, with any alternative requiring a transfer or two.
The night train connection exists between all three cities you list. You may get a sleeper, still when you arrive, I wouldn't.
One more thing....There is night train from Vienna to Warsaw, the terminus is Gdansk. This route Warsaw to Gdansk is both a day and a night train.
If you were going to Gdansk, then I would suggest doing the Wien to Gdansk route by day, ie some pretty interesting landscape and geographic/historical sights after Warsaw...that's what I would do.
As you are not, then do the route Vienna to Warsaw by night train, which is the option I would take too. Taking the night train, you'll see only locals, I would be quite surprised if you saw any tourists.