It wouldn't do either of those things. You only need 51 votes to confirm a cabinet nominee and the GOP has 52 senators. If the Democrats didn't vote for a single Trump appointee, we'd still have the exact same cabinet we have now.
And before you ask "so then why did they bother voting any of these picks anyway?", I return to my original point: to highlight the truly awful ones and engender massive public pressure campaigns on Senate Rs and the nominees themselves. A major reason why the advocacy against Sessions and DeVos was so powerful, if ultimately unsuccessful (because, again, the GOP has the numbers) was because they could be specifically singled out for their abhorrent positions and rhetoric. And to a lesser extent, Senate Dems did similarly for Puzder, Pruitt, and Price. But you can't raise that kind of outrage for the two dozen cabinet spots, let alone the hundreds of other Senate confirmable spots. You wear people out pretty quickly and your constant protest just sounds like background noise than substantial criticism.
And you can stop linking me that The Week article.