No it is not needed if all you have is a truly stock 512k with 64k ROMs and only the internal 400k floppy drive. (And it is not needed if you have a 512ke, which has the primary code of the HD20 INIT built into its 128k ROMs.)
But I have a serial HD20 hard drive external to my 512k, and so I have use for the HD20 INIT. I also have an external 800k drive for which I want HFS support, which is another reason to use the HD20 INIT.
I also have confirmed in the past that the HD20 INIT does in fact work fine with System 4.1 and various Finder versions:
viewtopic.php?p=54726#p54726
Indeed, S4.1 and F6.0 is the highest System/Finder combination you can use on a stock 512k with 64k ROMs.
So why are you experiencing problems with your HD20 INIT and S4.1? Perhaps because either the HD20 INIT or the System file you are using (or maybe even the Finder file) are corrupt. Because as I said, I can get the HD20 INIT to work without problem with System file 4.1 and Finder versions all the way up to 6.0. Try download S4.1, the HD20 INIT and a Finder file from another source and then give that a go. Make sure you have them on an MFS formatted 400k floppy too. Then let us know the result of your test.