No. It’s not a magic invisibility field inside. It’s a magic object that works only on living “intelligent” creatures. It also doesn’t work the same on different races. Only humans (hobbits are a subtype of human in Tolkiens lore) turn invisible. And because it’s magic it also turns their clothing etc invisible. So either Frodo and his poop is invisible or nothing is.
What do you gain by doing this? I trust both proton and mullvad to not fuck up their encryption so attackers can’t read your traffic even through one VPN. The second one doesn’t offer additional security here.
In your setup, proton will only know you use mullvad but not know which sites you visit in the end. Mullvad knows everything just the same as without proton. So the outer VPN doesnt add privacy either.
If you are suspected of a crime, forcing mullvad to disclose your identity/IP is enough and proton doesn’t help.
If you are worried about traffic correlation analysis, then yes 2 VPNs will help. But honestly for normal usage I don’t see the point of 2 VPNs.
And about the DoS fear. Just do it the other way round? Mullvad on the router, proton on the device? From protons perspective you produce the same amount of traffic, it just comes from a mullvad server. The outer VPN is the one where you have increased traffic due to 2 VPNs. But I am pretty sure neither will be a problem and tunneling a VPN through a VPN is not a TOS violation