A lot depends on who is making the decisions. Is Sweden running a separate War Plan, or will they coordinate with Germany. It also depends on the year.
If Britain lands troops in Norway, Sweden will be expected to keep them out of Sweden. The Germans believe in the attack, and would encourage an aggressive Sweden, so I can easily see Sweden trying to take Southern Norway and holding the high mountain lines in the north. Most likely, the UK still goes after the Ottoman empire, not Sweden. The goals, if not the execution of the operation, made a lot of sense for the Entente.
If no UK and 1914, Germany wants to slow the Russians in the East. They will likely encourage Sweden to at least attempt a diversionary attack in the North to try to draw a Russian Army North. My guess is that Russia would send the 4th Army north, and the 1st and 2nd Army would go on the defensive and give ground if the Germans attacked. For a major offensive, the Germans would probably want a Swedish Army in Prussia. Logistics by sea would be very risky. The Russian navy more stayed behind the mine fields than was defeated. Transporting Swedish divisions to Danzig and then supplying by rail is just so much easier.
Under Falkenhayn, he was big on decisive battles and knocking out smaller countries. If German GHQ believe a Swedish Army with German help could knock out Norway, it would have been approved and done in 1916, provide the butterflies are not too large by then.
So much depends on the POD, but basically, unless British forces land in numbers in Norway or Norway can be knocked out of the war in a few month campaign, you are right. Sweden defends against Norway and has the bulk of the Army fighting Russia.
IMO, Sweden joining is likely to be decisive for the CP. Based on year joining. In 1914, it gives the German more time to work on France and likely Russia reacting will save A-H the worst defeats. In 1915, Russia will have even fewer troops than OTL, and the German counter attack in likely works even better with at least one fewer Russian Armies facing them. A general collapse of the Russian line is even possible. In 1916, reacting to Sweden entering the war likely means Brusilov offensive is canceled or only a local success. In 1917 and 1918, it is probably to late to have a decisive impact.