No, it doesn't work like that. Norway is not a member of the European customs union. Goods moving between Norway and the EU are subject to customs checks and, potentially, tariffs. You can't just trans-ship Chinese goods landed in Norway onward into the EU without customs declarations, inspections, and all that.
Of course, private citizens can travel pretty much freely across the EU-Norway border. Goods can move freely in small, personal-use quantities (Norwegians certainly like to shop across the border at cheaper Swedish supermarkets, etc). But as soon as you start shipping stuff in commercial volumes, it is subject to customs just like any other Chinese goods coming in to the EU would be.
I elaborated a bit on this in a sibling comment[1], but let's say for example that the import duties on electric drills from China into the EU are set at 30%, but the same duty for Norway is 10%.
After signing a FTA with China Norway can simply import the drills at 0%, then re-export them to Germany at a rate of 10%.
Even if they can't simply re-export finished products a Norwegian company could buy cheap Chinese parts for making drills, then finish constructing them domestically and export them to the EU.
Even if they don't directly re-export anything from China Norwegian industry would be more competitive than its neighbors, e.g. a Norwegian paper mill might buy cheap acids for industrial from China that their neighbors in Sweden don't have access to. This would make Norwegian paper cheaper than Swedish paper, and Sweden would pressure the EU to adjust its import duties accordingly.
Thus the EU will start having to either treat Norway and Iceland more like China in terms of tariffs and import duties, or to treat China more like Norway and Iceland.
As for goods of mixed origin (manufactured in Norway but benefiting from Chinese inputs/components), that is indeed where things get complicated. And that's one of the reasons why trade agreements typically run many thousands of pages and take years to negotiate! But the WTO has pretty comprehensive "Rules of origin" to use as a starting point.
Right now this situation exists in theory, but in practice pretty much nobody in the EU has any cause to try to import something via Norway, since its trade deals are quite similar to what the EU itself has.
But the EU has huge tariffs on some Chinese products, including slapping China with 30-70% tariffs on basic metal alloys in some cases[1][2].
The difference can be so large that it becomes beneficial for you as a private EU citizen to drive up to Norway yourself to fetch e.g. basic alloys at lower prices.
Nothing remotely like this situation exists within the land borders of Schengen today. There's the agreement with Iceland, but as it's an island enforcement is much easier.
1. https://www.cnbc.com/2017/06/09/reuters-america-update-2-eu-...
2. https://www.theguardian.com/business/2016/oct/07/european-un...
If Norway started selling all its oil to China, then we'd have something. But the EU borders Norway, and China doesn't so there isn't much in favour of it. In addition, China doesn't border the EU, so I don't think it sees much value in a divided EU (as opposed to Russia). To them it is probably more interesting to distance the EU from the US.
You can read the full list of tariff concessions by Iceland[1], as well as the rest of the treaty[2] MFA website.
It covers anything from food, tools, machinery, to raw ore and metals to finished nuclear reactors. Almost all tariffs on Chinese goods entering Iceland are set at 0%.
This means that Iceland (or hypothetically Norway in the future) can import say cheap industrial acids from China, and use them to make finished products that could be sold to the EU market using existing EU/EEA trade deals that give preferential tariff treatment to EEA members.
That's the potential conflict I'm talking about. China's setting up agreements where a country with wide access to its internal markets has better access to cheap Chinese goods than other EU/EEA countries.
Which means that either the EU needs to slow down liberalization of trade with Iceland (and perhaps Norway in the future) least they essentially become hubs to evade EU duties on Chinese goods, which'll pull those countries further into the Chinese sphere of influence.
Or it'll need to make similar deals itself, or otherwise live with the resulting trade imbalance with Iceland and Norway becoming re-exporters of Chinese goods.
1. https://www.mfa.is/media/fta-kina/Vidauki-I---Tollaaetlanir-...
2. https://www.mfa.is/foreign-policy/trade/free-trade-agreement...
If Norway signs a similar agreement an EEA country with open land borders with the EU will have a FTA with China. At that point the EU would either need to never liberalize certain trade with the EEA least Norway become a shipping and distribution hub for Chinese goods into the EU, or accept that to get closer integration with Norway and the other EEA members.
There has been increasing liberalization of trade between the EU and EEA members, just last month the EU and Iceland agreed to drop almost all import duties on agricultural products[1].
In addition to all of that, with global warming gearing up the Northeast Passage[2] might become a viable shipping route between China and Europe, at that point shipping from China to Norway will be the shortest shipping route between China and Europe by far. Sailing from China to Europe via the NEP to Norway cuts time at sea and fuel consumption by more than half compared to going via the Suez Canal.
1. http://www.europarl.europa.eu/news/en/press-room/20170911IPR...
2. https://en.wikipedia.org/wiki/Northeast_Passage