The underlying problem with that strategy is not everyone signs up for Live when they buy an Xbox (unlike, for example, cell phones where your hardware is useless without a carrier subscription).
That would be an interesting set of stats to have: What percent of Xboxes never carried Live subs? How long of a Live sub needs to be carried, on average, to break even overall?
Given that the 360 is very heavily wrapped around the Live service I'm willing to bet the percentage of new units that did not generate a subscription is small. How many new units were replacements for failed units, though, and thus did not result in a new subscription but rather a continued one? Does that statistically matter?
I'd be interested to find out as well - though I don't have the time at the moment to research this. But I doubt the "Xbox Units to Live Subscription" ratio is anywhere close to 1:1 (counting both systems)*. $50 per year is a lot of money to some people who may only have a passing interest in playing online (myself included) or simply don't have the requirements to play online (i.e. broadband connection). What gets me online with the PS3, Wii and PC is that it is free. I subscribed for a year of Live back on the original Xbox; but never renewed because I couldn't justify spending the money (of course, nowadays Live has more to offer - but if you want it to just purchase games online, the free version suffices).
*
This quick article from 2009 shows 30 Million Units sold and 20 Million Subscribers. Discarding all variables (second units, for example) - that'll be an average of 1 out of every 3 Xbox's not hooked up to Live. But it's probably more complicated than that, so I'm not submitting that as hard evidence.
But yeah, MS wants people to use Live. Really want. That and software is pretty much how they make their money.