A referral is most useful when the person can credibly support your candidacy. A very thin referral is unlikely to create the same value as one from someone who has actually spoken with you enough to form a view.

That does not automatically mean it hurts. The bigger concern is relying on the referral as if it guarantees anything, or asking the person to write claims they cannot support. The application still has to stand on its own.

If the person volunteered, you can make it easier by sending a concise resume and a few factual points about your background. Let them decide what they are comfortable saying rather than scripting praise for yourself.

Treat the referral as context, not a substitute for fit or qualifications. If you have time, one more substantive conversation can make the relationship stronger. See the consulting networking guide for the broader process.

A referral from someone who cannot say anything specific always felt pretty weak to me.

I would send the resume and let them decide how strong they are comfortable making it.