Your terminology is just a little confused here. Root Position doesn't refer to the lowest note in the arrangement - it refers to a chord arranged such that the Root is the lowest note. So it isn't possible to have a chord in 3rd Inversion and Root Position at the same time. The Root is nothing more than the letter-name or scale degree after which the chord is named.
I didn’t proofread & may have implied something I didn’t intend. I thought 3rd inversion would have the seventh as the lowest note, next note the Root, then the third & fifth (of a Major Chord).
My teacher used ‘Root Position’ when describing inversions to differentiate from the Root, but I’m more concerned about the inversion (tho I realize now ‘Root Position’ may not mean what I thought). Time to dust off some books.