Can I send money to someone even if I don't have their mobile number?

Yes, Truecaller Pay lets fund transfer funds the old school way too, so that you can send money to friends who are not ready for Truecaller Pay yet.
To do so, go to the Send money option on the home screen.
Select Beneficiaries tab Enter the user's account number and IFSC Code.
Use this option and send money to them instantly.