Sokrates: Given that Poles were the only country to stop the Ottomans alone yes they were succesfull, see Battle of Khotyn
The Polish-Ukrainian-Lithuanian army numbered 30,000 (18,000 cavalry, 12,000 infantry) and further 25,000–30,000 Ukrainian Cossack army, led by hetman Petro Konashevych-Sahaidachny (mostly infantry). So have of the allied army were Ukrainian Cossacks.
The army, following a common Commonwealth defense when facing large Ottoman armies, employed deep defences by building separate field works in front of the camp's defences. These field works were designed to allow the use of cavalry counter attacks, especially crucial for the Commonwealth relying on its elite Polish Hussars and Ukrainian Cossacks http://en.wikipedia.org/wiki/Battle_of_Khotyn_(1621) There was a Battle at Cecora in 1620 (just a year before) between the Ottoman empire and the Polish-Lithuanian Commonwealth. What was the outcome when the Ukrainian allies were not there like in Khotyn?
Hetmans Zółkiewski and Koniecpolski led the army to Ţuţora (Cecora in Polish sources), a commune in Iaşi county, Romania) to fight the Horde of Khan Temir (Kantymir). The army numbered over 10,000 (2,000 infantry and almost no Cossaks cavalry)
During another large assault on the 6 October, most of the magnates and nobles started to flee north, leaving infantry and camp. Thus, they sealed the fate of the whole expedition: most of the Polish troops got killed or were captured. In the ensuing battle, Żólkiewski was killed and Koniecpolski and many others (Samuel Korecki, Mikolaj Struś, Mikołaj Potocki, Jan Żółkiewski, Łukasz Żołkiewski), Stanisław "Rewera" Potocki and Bohdan Khmelnytsky were taken captive. Żółkiewski's head was mounted on a pike and sent to the sultan; duke Korecki, having often meddled in Moldavian territories, was executed in the Istanbul prison. http://en.wikipedia.org/wiki/Battle_of_%C5%A2u%C5%A3ora_(1620) The monkeys left the infantry to die - what kind of army command is that, Sokrates? Have you been in Khotyn? Amazing castle: 
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