First, "inversion" only distinguishes what's in the bass. The voicings above the lowest note are not changed in any way. Whether the total sound is C E G, C E G G C G C E, or C G G G G G G E, it's all root position. E G C, E C G, E G C G G C is all 1st inversion.
It's not uncommon in lots of music. First one off the top of my head is "This Old Heart Of Mine" by The Isley Brothers. Jamerson plays an E under the C chord around the third measure. McCartney has said he's quite fond of putting other chord tones under the the chord, and often says he copped the idea from Brian Wilson.
The intro to "Angel From Montgomery" by Bonnie Raitt (John Prine wrote it)- the second chord is an A with the C# in the bass- so it's first inversion. "I'll Be There", the Jackson 5 song- The first verse is full of non-roots under the chords. The first part of the progression is |D | A/C#| Bm | F#m/A|. The C# under the A chord and the A under the F#min are what gives the line its movement. Also listen to "A Whiter Shade of Pale" to see how the line moves by not playing roots.
John