Creating group policy registry keys to prevent users from turning Windows Defender back on does seem rather drastic, but obviously Avast does not think it is a good idea to run Windows Defender alongside their antivirus. I'm surprised by all the opposition:
https://forum.avast.com/index.php?topic=189162.0.
Like you, I used the old Windows Defender antispyware along with a third-party antivirus for years without any major disaster. How many threats did Defender stop? Zero, but it made me feel more secure. Then one day, AVG antivirus detected something. I visited the old AVG Forums and found that many others were getting the same detection, and that it was a false positive caused by interaction with Defender. Not long after that, AVG released a program update that turned off Defender. (I gave up AVG two years ago and do not recommend it.)
Someone in the Avast thread suggested that using Defender should be harmless if you turn off the real-time protection and only use it for scanning. Well, after giving up AVG I tried Panda for a while. I got a false positive the very first time I ran a full scan with Defender! (For on-demand scanning it's hard to beat Malwarebytes Free, but there's also Microsoft Safety Scanner:
https://www.microsoft.com/security/scanner/en-us/default.aspx.)
Now I'm using using Microsoft Security Essentials, which is much better than is generally believed. Installing MSE disables and replaces Defender, and I have not even attempted to turn Defender back on, having learned my lesson. The answer to your question is no: It does not matter if Defender is off. If you are going to place your faith in Avast, then you should trust their judgment regarding Defender.