We don't actually have a responsibility when doing lead sheets like this to show the exact positioning of the chord other than the fact that it comes before the syllable. Check out Music Braille Code 2015 example 36.3.3-1 for an example like the one you sent. The second measure of the MBC2015 example begins with a quarter rest and an eighth rest, the chord sounding on the initial quarter rest of the measure. The chord name is still simply placed two cells to the left of the initial character in the word. So whether it's one rest before the syllable or two, it is brailled the same way.
I've attached the measure you asked about here -
If you decide to begin a new parallel with the pickup G3 then sure. You can braille the Cdim7C on the previous parallel and begin a new parallel with "I'm" and the C chord placed under "feelin'" Either way is acceptable.
Hope that helps!