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.
Back in the day, one of my friends built a Spectrum-compatible computer from parts, using a piece of laminate board without foil, some thin wires, and a 60W soldering iron, in a college dorm room.
The fact that it can be done does not make it particularly convenient or easy, especially for a novice (my friend was pretty experienced with electronic assembly by then).
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.