Given I couldn't even tell from the picture wether you'd bought a C or a G revision, I'm really not the person to give advice but I think the C did have different chips to the original breadbin models.
Then again I think I read (on a collector site) that some C-64Cs were made by using original version mobos and chips left over from the previous production run; Commodore's production techniques were, odd at the best of times.
kd7ota's post seems to explain the difference between the two SID chips BTW.