Not really. Many college students work at part time jobs to make ends meet .... or at least used to when jobs were available.
Some, yes. Some, no. Many do this intermittently. At any given moment, the number of college students who are
not in the workforce includes many students who were working a few months ago, and/or students who will be working a few months from now, but are simply taking some time to concentrate on their studies at the moment. More often than not, many students will simply choose to not work if it's at all possible, because
the high demands of receiving a college education make holding a job a liability for educational success. They're in class 20 hours a week, they're studying 40 hours a week, and they're supposed to hold a job in the meantime also? Many of the young people I'm meeting nowadays are telling me that they are choosing to not work during the academic year (or work extremely limited hours, or sporatically), because they can study more while having a less chaotic schedule, which leads to better academic performance.
Once again, none of that changes the fact that
lower high school dropout rates and higher college attendance rates will necessarily result in lower force participation rates among 16-24 year olds.
Now, far too many are saddled with tons-o-debt that they will never be able to a pay off.

If you're really trying to imply that dropping out of high school to flip burgers is the way to pay for college, you're lost your ******* mind.
And what is the impact: delay in family creation and home buying.
People are delaying these things for alot of reasons. First on the list is the fact that people just don't want to listen to what other people tell them to do with their lives. The trend started with those of us at the youngest end of the Gen X crowd. We didn't run off and get married just because we were expected to. We didn't necessarily run off to buy a house just because grampa fed us some propaganda about how we should "put down roots." Our younger siblings and such were inspired by our example, and now the Millenials have decided to say ****-all to other people's notions of what to do when. Getting married is seen as a formality for many younger people. Having children is seen as an expense and responsibility to be carefully weighed and considered before doing. Oh, and there was that nasty episode that you might have heard about....it was called the housing bubble burst. It's made many younger people reevaluate the financial viability of investing in a house, and has made them hyper sensitive to the timing of the market trends, and to factoring one's long term career and financial plans.
The economy is in a downward spiral due to excessive debt. Fake stats provided by the Feds don't make this any less of a fact.
I won't disagree that the economy is in bad shape. But you're citing all the wrong indicators, and inferring a bunch of false causes.