I think that just like Poland at a time, Iberia would have to be balkanised into small duchies for such independent monastic state to emerge.
If balkanized, it's likely Hispania would have been
1)Integrated sooner or later within another kingdom (the most obvious the kingdom of France up to the XI century as the catalan counties were)
2)Unable to resist (not talking about reconquering) Muslim Spain and putting the whole military order thing butterflied in the peninsula for a while.
3) The spanish feudalism quite prevented a great balkanisation : the king had a greater role and the lands weren't fully given as they were in France or Germany.
The little nobility, aslo, could be under direct royal influence without passing by other vassals.
It was sometimes based more on communauties/suzerain than vassal/suzerain relations.
Finally, the muslim presence in Al-Andalusa nd the subsequent raids pushing quite far to the north forced the nobles, king and nobility to keep some coherence in order to resist.
I don't think you'll have a greater "balkanisation" that it happened during the XI century with many competing states (Galicia, Leon, Castile, Navare, Aragon, Barcelona-Catalonia).