Don't worry about everyone using all the features, only the most important ones will. And be sure you're actually doing something for the user in exchange for their time and data.
Here's a statistic from several years ago that illustrates the issue well:
[by the end of 2009] about 80% of all Twitter users have tweeted fewer than ten times. [source]
There's that 80/20 rule again. Twitter was exploding with activity by the end of 2009. And 80% of it's users probably did nothing more than squat on a user name and leave that silly little egg avatar in it's default state. They didn't bother with the increasingly detailed user profile Twitter provided.
Here's my wild speculation: The percentage of users who completed all profile options during that time was in the single digits (and probably still is). But that's not the point. If you want users to be engaged, you want the really engaged ones to feel like you care about them and are giving them a voice. That tiny percent of deeply devoted users will make a big impact.
Take a look across the SE sites. As you noted, there are tons of question askers and lurkers who fill out the bare minimum (Office Space, anyone?). But look at it from another angle. There's that less-than-ten-percent group to thank again. They pour out their experience to answer questions, edit submissions, provide quality ranking, filter out junk, and gain profile cred along the way. Those select few crazies are building SE's killer search rank.
There's two sides to the coin. On the one side, you're rewarding the user by making them feel like part of the community. Maybe you're really good and you use that expanded profile to better tailor your service to their needs. There's the other side of the coin: You're also cataloging all that insight and capitalizing off of it in some way. If you're not, you will or should be. Or you'll lose.
Don't forget 'social sign in'. Allowing your users to log in with a social media account is a very fast way to get an expanded profile. It saves the user time and gives them one less log in to remember. And you are more likely to get rich data about the user. Jan Rain was a leader in this space, and still puts out some good info on the subject.
Just remember to give something back to the user. 'Gamification' is the buzz word, but it's really just about making sure the user isn't giving you time and data and getting nothing in return. Every service is different, so the model has to change too. For SE, it's about users who are passionate about a subject and want a little recognition in that space. They knocked it out of the park! Facebook created a whole bizarre, voyeuristic second life out of stealing your data. There's some backlash, but look at their average engagement! More power to ya, News Corp.
Once you figure out what your users want and/or need and how it relates to your brand, you'll know how much to ask and what to give in return.
I don't have any. You're going to have a hard time finding research on a question like "is completing a profile good". The data you're looking for is likely hidden behind internal test data. And it would change from one site/app to the next.
First you need to define measurable KPIs. Are you looking for conversions, time on site, average page views, number of return visits, etc? Once you know specifically what you're looking for, reach out to some non-direct competitors and see if they've collected similar data.
In the case of your intranet site, you probably aren't going to get much of a sample. Try just doing some guerrilla research. Who do you intend the expanded profiles to benefit and how? Identify a few people in the company and do an informal interview with them to see if your assumptions match their goals.
Gamification-- I like wearing different UX hats...