The 2nd class pass costs $165 for 3 days, $30 per additional, 1st class pass $215, $35 additional, according to one web page. Given that, we drop the E17 fare from Seville->Granada from the pass.
www.renfe.com shows these fares, in Euros
Barcelona -> Madrid 2nd E44, 1st E58, Night 2nd E40 1st E53
Madrid -> Seville AVE 2nd E64, 1st E95
Granada -> Barcelona E47 Night E49
I'm ignoring sleeper compartment cost, since that will be the same in with or without a pass.(?)
Thus, the total for 2nd class, with night trains, individual purchase, is E153, and 1st class E197.
There are a bunch of unknowns here: cost of seat reservation with pass, surcharge for AVE, etc, exchange rate in July, additional pass use (such as stopping off in Cordoba). So is $165 + extra fees < E153? Or $215 + extra fees < E197? Borderline, and dependent on extra fees and other unknowns. Plus there may be errors in my numbers. I can see why you aren't sure.