Then that chord would be written C9/E, standard guitar symbol notation. The Bb makes it a dominant function chord (V9/IV -> IV in C maj) and octave displacement of the 9th doesn't matter although it would sound drastically different in a closed vs. open voicing.
I still hold that C2/E is ambiguous out of context. Most likely bad harmonic analysis and not accounting for accented non-harmonic tones.
