I found the answer to this question from a few years ago, but a lot has changed with Google since then. Would a technique with the one described here still work?
Things have indeed changed since then:
A year later in 2012, Google released an update to its search engine algorithm that was aimed at leveling the playing field for websites that relied on using keywords in their domain names, otherwise known as Exact Match Domains (EMD). There's a good breakdown on it here.
Prior to that, SEO black hats were registering large numbers of domains that were rich in keywords, and providing thin or unrelated content for them, with the expectation that search engines favored them in keyword searches. Now Google no longer weighs keyword rich domains over others, unless recognized as a brand-name. There's a very detailed report on this here.
The second part of this strategy regarding building small websites with unique content is often referred to as microsites. The general consensus is that the amount of time spent on building and maintaining these individual sites might be better focused on the main site, as covered by Matt Cutts in this video: What's your opinion on microsites?, in which he also references this article: Microsites. A Bad Idea Most of the Time.
A few microsites might help your client if their content is truly unique and offer some value not available on your main site, but still relevant to it. Lots of microsites however might be perceived as "spammy" by Google, which targeted that in its Panda update. See this for more on that: Google Forecloses On Content Farms With “Panda” Algorithm Update.
I am a web developer and have a client who wants to hire me to do this, but I'm not sure its going to help or hurt him.
You might let him know that this SEO strategy is somewhat outdated, and although there could be some benefits, the amount of effort and expense might be better spent towards improving the main site and building its brand-name and recognition.