When was this ?
I enquired in September 2020, they did not back then, even with letter from the HR (maybe it depends on the Branch).
Then I went ahead and opened a Salary Account in HDFC. No questions asked, though the experience sucked.
Fingerprint reader did not work at the branch and they took 5 days to activate my account.
IDFC Savings bank account was open within 2 minutes 🤣