We use intrusive r even, and perhaps most strikingly, when attempting to speak or sing in foreign languages.
Here’s a YouTube clip of a pubful of English people singing Que/Y Viva España. You can just about detect the r in ˈvi:vɑːr eˈspænjɑː. Faced with a final open vowel at the end of viva, followed by another vowel at the beginning of the next word España, it would require a rather sophisticated effort for us not to link them with an r-sound.
(Since the karaokeers are nonrhotic, they naturally also sing por favor as ˈpɔː ˈfæˈvɔː. Please don’t anyone write to tell me that in proper Spanish it’s i ˈβiβa esˈpaɲa, poɾ faˈβoɾ.)
That was untrained karaoke. But even trained singers do the same thing. The choir I sing in is currently rehearsing the drinking song from La Traviata.
Godiamo, godiamo, godiamo,
la tazza e il cantico
la notte abbella e il riso,
in questo paradiso,
ne scopra il nuovo dì,
si, ne scopra il nuovo dì.
For each song our choir plans to perform, the music team very nobly prepare rehearsal tracks for us to listen to as we learn the words and music (blog, 19 January). Here’s a clip of the very last phrase, from the tenor 2 rehearsal track. It contains a very clear intrusive r between scopra and il.
This also serves as a counterexample to the claim sometimes made, that a preceding r (scopra) blocks the operation of the r-insertion rule.