I have 77 AUR packages installed as we speak. There are no issues with AUR and Manjaro's delayed packages. AUR are source packages. They will compile against whatever is installed.
Occasionally an installed AUR package breaks because I don't update them automatically and the system libs have moved too far away from the binary I compiled. I rebuild it and that's it.
Obviously, you shouldn't install anything from AUR that will take the system down with it. This is true for any Arch distro.
In theory an AUR package can require an Arch package version that's not in Manjaro yet. I've never had that happen in 4 years and dozens of AUR packages. If it ever did I'd either install an older version of the AUR package or get a flatpak version.

