It's said that EEA countries outside the EU could 'unilaterally' apply some kind of emergency brake to curb immigration, and they cite Article 112 of the EEA Agreement.
Unfortunately, no they can't. As a member of the EEA outside the EU we would be bound by the EJC decisions rather than the EEC, but one of the EJC's primary roles is to ensure consistency on how the EEA Agreement is implemented with regard to EU countries. The EJC are going to use the same criteria on whether our safeguards are acceptable as the EEC for that reason. If they don't agree on our curbs, they'll refer it to arbitration and possibly ultimately the European Court of Justice.
The question has to be asked, since even EU countries are signatories to the EEA Agreement and therefore so are we, why haven't we taken the arbitration or ECJ route already? Could it be that the EEC have rejected our claim that we could apply safeguards, and any legal challenge would fail because the ECJ would uphold the EEC's decision?
Any arguments that say that we have some kind of immigration control while being out of the EU while a member of the EEA are fundamentally flawed.
The EEA is the single market though isn't it, which is part of the EU. Norway, although not part of the EU is governed by the EEA and therefore has to conform to the freedom of movement. I don't think it is suggested by most that we would have access to the single market and have control over immigration. It has been made absolutely clear that the EU would not allow us to cherry pick the parts of the EEA that best suit us?
It is clear to me that the UK would have to negotiate new trade deals with the rest of the world should we leave and that is primarily what the focus of the trade argument is about. No ones saying that we can't trade in the EU either. It is just that we would have to negotiate with all 27 nations and incur a tariff imposed on us for the benefit of trading in the EU, and I don't feel we would we be paying 10%+ tariffs on exporting our goods to the EU, nor do I think the UK economy would collapse if we were paying those tariffs. It is worth remembering that a lot of our import comes from Germany, France and Italy and that amounts to a lot of jobs and commerce on their part, so there would be room to negotiate a better deal from my understanding. Any talk of the EU wanting to penalise us for leaving, and setting an example to the rest of the nations need to tread carefully as some of the biggest nations have a lot of goods exported to the UK market that could cause big loss of jobs and money.
Of course the EU accounts for 50% of our trade (actually think it is less than 50%), with the rest being global trade deals accounting for 56% of our trade. My opinion is that if other countries can successfully negotiate trade deals outside of the EU, then so too can the UK. It is clear however that there would be a financial hit to the economy, but for how long is the question.
Bottom line is, we would have control over immigration, but not on the single market, which is essentially what the EEA is.