Short answer
For the genes a wellness panel reads, yes, saliva carries the same DNA as blood, and unlike blood it needs no needle and no temperature-controlled transport, which is what makes at-home testing possible across India.
The DNA in saliva is identical to the DNA in blood, so for genotyping it is an equally good source. Saliva's practical advantage is huge in the Indian context: it is stable at room temperature, so a kit can travel to a small town and back without the cold-chain logistics that blood requires. Some specialised clinical tests still need blood, but for lifestyle and wellness genotyping, saliva is fully sufficient.