TIL bash-completion can load completion files lazily. pacaur should do that.
I believe it's achieved by placing the completion file into /usr/share/bash-completion/completions/.
Seems to be something that should definitively be implemented, although I'm not sure if moving the completion file would be sufficient as I'm not familiar with lazy loading. Thanks for reporting.
Closing as the config file has been moved in /ush/share/bash-completion/completions in pacaur v3.0.x.
Note that a new, more complete completion file is currently worked on (see issue #65).