No. They have literlally have no incentive to give you that referral if they don't know you. Better reach out to other people in your network (friends of friends, alumns from your school, etc.). No need to only reach out to partners. Better folks around or just above the tenure level for which you're applying.
Don't ask them for a referral, but for help. Help in the preparation of your application, help to understand the ways of working, etc. At the end of a 20min call you can ask what the best path forward for your application will be. If they have a strong impression, they'll get the hint and offer to pass your docs through to the HR team.