I don't know anything about that specific battle or conversion of the Turks in general, but throughout history religious conversions tended to occur from the top down. Generally, a ruler or noble would change religions, usually for political reasons such as a military alliance or a marriage alliance. Often, that person's conversion would increase the influence of that religion in the region, by encouraging other prominent members of the community to convert as well. If the ruler/noble was overthrown or renounced their religion within a decade or so, the religious shift often wouldn't take hold as that's not enough time for the population as a whole to change over. However, if the ruler/noble kept the new religion and maintained power for a long time, and particularly if their heirs kept the new religion, conversion was inevitable.

So, in the context of a specific battle, yes, that happened... kind of. Losers would be forced to accept various terms to keep their lands and often their lives. It was not unusual for those terms to include conversion, particularly if the loser had been captured and could not afford their own ransom. In some cases, conversions after battles even occurred for the victors. For an example of that, you need look no further than the Battle of the Milvian Bridge, where Constantine converted to Christianity after winning the battle. However, in most of the cases the 'conversion' was pretty superficial. Generally it would be a few nobles/rulers who officially changed religions, but most of them probably did not really embrace the new religion in their hearts. The true conversion would proceed from there over a very long period of time. So, my basic answer is that battles like that can certainly be the definitive start of a conversion, but they do not result in the wholesale conversion of the entire population in a single instant.