Not necessarily, no. There are various conditions, such as androgen insensitivity syndrome or Swyer syndrome, in which having XY chromosomes may not lead to male development and may even, in the case of Swyer syndrome, lead to the development of female genitalia, although not functioning female gonads.
Intersex conditions are varied, variable and complex, and the best way to include intersex athletes in competition isn't always obvious. But it's certainly not about chromosomes. Phenotype, not genotype, is what matters.