It seems likely to me for a variety of reasons.
First of all, covering distances over the generations: Imagine a tribal people of small family groups that raise kids who go to adulthood, these kids strike out to form their own groups. How far would a population spread in several generations? Let’s say 10 miles per generation, as these people are hunters and gatherers and would need a territory large enough to support themselves. Such distances are common for animals such as cougars, wolf packs, etc. Now after a couple of millennium, and assuming 20 years per generation, the spread of the species would be very large—thousands of miles—all without roaming more than ten miles from the birth home for each individual.
The continuing spreading of the African Rift. Madagascar split off first, and then Arabia later. The Rift is still very much a work in progress and 100,000 years ago the Red Sea would have been much narrower. Also, repeated world glaciation would have dried up the sea. In the last full glaciation 20,000 years ago, the world sea level fell 400 feet. Walking rather than swimming into the Arabian peninsula would have been possible. However, even if a water barrier still remained, it has been proven that Australian Aborigines used boats to get to Australia about 50,000 years ago.
Finally, the genetic variances in us humans point to separate evolutionary pressures due to environmental factors that took time. Light skin for Northern Eurasians. Wide flaring nostrils and tight curly hair for those in steamy equatorial climates. Resistance or susceptibility to certain diseases or genetic adaptations (sickle cell—malaria, cystic fibrosis—tuberculosis) that point to repeated exposures over time.
"Following the prehistoric breakup of the supercontinent Gondwana, Madagascar split from India around 88 million years ago, allowing native plants and animals to evolve in relative isolation."
“Lets say 10 miles per generation, as these people are hunters and gatherers and would need a territory large enough to support themselves.”
Might the plains Indians, before the arrival of horses, have some similarities to these people? If so, a band might need a lot more than ten miles.
Ice Age world map with the ocean levels reduced by about 320 feet. Notice no Persian Gulf and an Isolated Red Sea. I believe the Red Sea would have completely dried up. The Mediterranean may have been been in sections and dried to some low levels.
Passage through the Straits of Malacca would have been blocked until about 7,000 years ago when the seas rose enough to allow passage.