I am using a logic gate "simulator", like this one, to build the gates in the nand2tetris course.
For those of you more learned than I am, do you think I will miss anything important if I choose not use the HDL/Test Script/Compare file approach?
I like Logisim better, and it's free. It's powerful enough to implement the Hack computer.
You should do the HDL and testing because you can't know how well your more complex parts are satisfying the requirements it you only do them in a visual logic simulator. For example, when you make your ALU in chapter 2 you can poke at it in Logisim, but you can't evaluate it as thoroughly as the HDL test scripts will.
It's also amazingly cool to see your Computer running in the Hardware Simulator executing a program that you wrote using the Assembler that you wrote!
I recommend using the visual tools to prototype the gates as you start developing them. I expect that you will find that writing HDL gets easy enough that you will stop using the visual tools as you progress through the book.
 Except for the graphics screen—you need to use text only output.