No, Aadhar is not mandatory to generate UAN. You can generate UAN without Aadhar, but for the benefit of employees later on, you have to do KYC - Aadhar, bank account number, etc. Even the PF authority provides a non-Aadhar form to withdraw benefits.
For ESIC, Aadhar is compulsory as they provide treatment only on the basis of Aadhar. ESIC has stopped the biometric "pehchan" and now they are not providing ESIC cards in Delhi - and later on, they will stop it in every location too. So, please suggest to your employees to make their Aadhar as soon as possible.
Regards,
Nishu#