A major reason, yes, but not the only reason. Apple’s infamous “hell freezes over” announcement of iTunes for Windows came in October 2003. As you can see on the graph, sales didn’t really take off until 2005.
So while lack of Windows compatibility was certainly an obstacle to the iPod's popularity, gaining it was not the single catalyst to its success.
That's because in 2003 it still required firewire which basically 0 PCs had. Furthermore 2005 was when they released significantly lower-priced models like the nano and shuffle.
And the 4th gen iPod with the click wheel came out in 2004 which is when the larger iPod models really hit their stride. The iPod was not an obvious world-beater out the gate.
So while lack of Windows compatibility was certainly an obstacle to the iPod's popularity, gaining it was not the single catalyst to its success.