tl;dr version: Trying to learn electronics at the module level will give you about as much knowledge about electronics as someone who points to their monitor and says 'this CPU doesn't work!' has about computers. As long as the instructions/tutorials get everything working, you're good. But as soon as things go even slightly off-script, you'll be lost and have no idea how to troubleshoot things.
The issue is not the modules, but the underlying electronic components themselves. I started back as a wee lad with one of those 150-in-one kits and it was a great way to learn as a kid. From there I moved on to the various 'cookbooks'. Then I was able to follow projects in magazines etc. All doable over the course of a year or two depending on how motivated you are.
If I were starting from scratch today, I'd probably use an Arduino and follow some basic circuit tutorials online. (i.e. wire up breadboard circuits to the Arduino using it for power, digital input/output, ADC etc) If you only want to do digital electronics (i.e. true/false logic input/output), you can get by without too much analog knowledge (i.e. reservoir and noise filtering capacitors, using resistors to tie lines high/low etc.) but as soon as you want to interact with the real world (i.e. driving banks of LEDs, temperature and other sensors, motor control, etc) you really, REALLY, need to learn about analog circuits. No need to become an expert, but you want to get the basics down so you have an idea what's going on when things go wrong (and they will!)
It shouldn't take too long but you need to get below the modules and focus on the individual components (i.e. the basics of voltage/current, resistors, capacitors, inductors, diodes, transistors, amplifiers and then move on to ICs and modules etc. and not just what they are/do but get some basic knowledge about how to measure and troubleshoot issues with them) to understand at least conceptually what things are doing at the component level. Then those modules won't seem like such a mystery when problems arise.