If my marriage license was never recorded, was I legally married?

Yes, if all the other requirement were met.  The Arizona Court of Appeals has held that the failure to record a marriage does not invalidate a marriage.  The case is State v. Guadaghi, 178 P.3d 473 (App. 2008).  The Court reviewed the statute on marriage, which requires two witnesses who sign the license.  It is then up to the official performing the wedding ceremony to file the license with the state.  If the official doesn't file it, there are penalties against that individual, but the marriage is still valid.