Netflix does not publish viewership information. But a large ISP could run DPI on Netflix traffic to determine what content is being viewed. And since many ISPs have their own TV product, they would be really interested in that information themselves.
But if Netflix streams at TLSed, then good luck figuring out Archer from The Lust of the Dead.
Not necessarily that hard. TLS won't hide the sizes of the files being downloaded. You may even be able to estimate the size of each segment as they're downloaded, which should give you a pretty accurate fingerprint.
You'd need to spend resources to play each movie with different devices and bandwidths and record the traffic pattern, which raises the bar a fair bit.
On the whole I doubt you would have a high probability of identifying any specific show. Even if you are able to cull 75% of the possibilities (i.e. 4 bits of entropy) that still leaves lots of shows (total ~1000 tv series and ~5000 movies by one source), plus all the noise of people pausing/switching, skipping credits, etc.
CBR does kill it, though, and "uniformly distributed" is too big an ask.
Off topic, but an interesting thought: you know the HBO intro? With the static? That static is the hardest thing in the world to compress, and also the thing that viewers care the least about having compressed accurately. That's weird, I wonder how true it is across the board -- certainly artifacts can be jarring in flat shaded cartoons...
For DSL typical packet MTU is 1400-something. Why do you ask? It doesn't really matter because the upper level proto is oblivious. You can just use b/s instead of packets/s if you want to compare bitrates.
There are special encoding modes in 264/265 for handling animation. I'm not aware if there being modes for the intro except that it is monochromatic.
I was wondering how finely you can get the total filesize if it's encrypted. Can you just count fixed size packets, or can you figure the length down to the byte? Makes a big difference if you're trying using that to fingerprint the shows.