Absolutely. I can personally attest to the fact that $5 soldering iron is good enough for most common (non-smd) jobs. I've seen people do smd soldering with a big chisel tip, even a soldering gun, but it takes training. But I get OP's point. It's extremely frustrating if not impossible to do the job if the iron is super bad, if the flux or soldrr is bad etc.

For a beginner, a soldering station or a high-tech iron is absolutely not necessary. You just need a non-garbage iron, some decent quality lead-rosin solder and a decent amount of flux (cheap rosin would do). Nevertheless, having high-end tools will make things much, much easier and simpler. But at the same time, I believe you'll get a great training if you learn things the hard way.