I think the question is badly raised. The question is not how Catalonia joins EU, but if it is possible to EXPEL Catalonia, as Catalonia as a part of Spain is now is a part of the EU (including EU citizenship).
So there are different possibilities:
Catalonia makes a declaration of independence but is not recognized by Spain. Thus, at this moment Catalonia would be part of EU despite the political tension and despite the acts of sovereignty of Catalonia and despite the police and legal repression of the Spanish state over the Catalans.
Spain recognizes the situation. At this moment the question of if Catalonia should be part of EU appears. But NOW is part of EU. It should be first expelled? First, large and unclear legal considerations should be taken into account, which probably it took years. Second question: It would benefit someone expel Catalonia?:
- I t will harm the same Spain (70% of Spanish goods traffic to Europe is transported by Catalonia)
- It would damage the overall European economy for the same reason, and by the reason of the own industrial and scientific capacity of Catalonia, the most developed region in Spain in many indicators.
- After Brexit EU the last thing the union wants is that more countries leave the EU.
If Catalonia wins his independence obtained in spite of the authoritarian opposition of Spain Government and by Democratic methods, and without violence, it would be a democratic lesson for the world and for Europe. Democracy should not scare us in any way, and the international laws of self-determination is mandatory.
There are regions in other countries in EU that could demand the same that Catalonia? May be, the History is dialectical and we must to accept political changes if democratic. But do not forget that may be other States do not have the same political blindness that Spain, which has practically not left more option to Catalonia than to fight for its independence. Despite that half of the actual States in Europe have become independents in the past, I do not foresee an epidemic of independence from other regions in EU. ....but Spain is a different question. If Catalonia becomes independent Spain will be disintegrated in several years. (by the way, this question was predicted by a history mathematician 80 years ago together with the URSS disintegration ).