Will a $16 mic work? Yeah, probably. Will it work well?? That's a crapshoot.
Professionals don't spend 20X as much on equipment just because they like spending more money. There's usually a very good reason for it.
Those reasons can include one or more of the following:
Durability. Cheaper stuff tends to use cheaper materials. They may look the same on the first day, but connectors fall apart, cables fray, etc. Note that this isn't always the case. Sometimes the better stuff is more delicate because it needs to be for performance reasons, which is another difference.
Reliability. Similar to durability, building something reliable costs more. Cheaper stuff sometimes has the habit of simply failing during normal use due to cheaper manufacturing standards.
Quality. Microphones are a piece of gear that will make the most difference in how things sound. Yes, any mic can pick up sounds, but they all behave differently. Getting a small mic with good linear response is not as simple as it may look. If you've ever worked with crappy mics with wild frequency response, you'll find them near impossible to get any gain before feedback at certain frequencies. They may sound almost the same, but require massive EQ chops just to work. Not fun at all!
Consistency. This is the big one. The problem before of frequency issues can be wildly different between mics. On the cheap mics, yes, they will make sound. But Mic A might sound and behave completely differently than Mic B of the same model. If you only have one mic, that's not as critical, at least until you need to replace it. If you have a fleet of mics that may need to be switched around, the more consistent they are, the easier your life will be.
