According to Titus Livius (Livy) the patrician families were founded during the reign of the first King of Rome, namely Romulus. Livy says of Romulus in his Ab Urbe Condita, 1.8:
He created a hundred senators; either because that number was adequate, or because there were only a hundred heads of houses who could be created. In any case they were called the "Patres" in virtue of their rank, and their descendants were called "Patricians."
From what I can deduce, these families did not necessarily come to be patrician because any of the individual members acquired the rank of consul, but came to be so due to their proximity to the first king as advisors. Their prominant position in Roman social life certainly gave them an advantage in acquiring the consulship as it was reserved solely for the patricians until the institution of the Lex Licinia Sextia in 367 B.C.
I had a look at a list of the known patrician families on Wikipedia and searched through the known list of consulships which confirmed the Foslia, Potitii, Pollii and Siccia gentes never produced a consul. So yes, it would appear that there were patrician families which never produced a consul and those families are bound to be more obscure in the historical records in comparison to those families which managed to maintain exclusive control of the office.