When I first read this, my answer straight off the mark was 'No'. If the Project Manager accepts a quotation, then that is the end of it.
However, there is a slight subtlety here (and I will put the key words in capitals, as I can't underline or bold them) : if the PM accepted the quotation for the additional work to be REMEASURED using the same rates as in the original BoQ, as opposed to effectively accepting a lump sum (based on FORECAST quantities times the same rate), then the former might be true.
However, the devil will be in the detail of the Contractor's quotation i.e. what did the quotation say.