No, because the Senate GOP knows that if they pass just anything it won’t survive the reconciliation process in the House, especially if according to your scenario even Boehner’s bill doesn’t pass...why then would the House pass the Reid bill?
Once the bill has Reid's name on it instead of Boehner's and comes back to the Congress it will get most or all of the Democrats votes and it will need only 25-35 wobbly (RINO) Republicans for passage.