well it would open another front for the Russians and would likely send Finland into full revolt, also Sweden had about 6 division of infantry and a division of cavalry that was ready to go and the ability to call up an addition 6 divisions of infantry from reserves. While its just a drop in the bucket compared to what Russia could field, it would also force Russia to divert units away from the front with Germany and Austria-Hungry to keep Sweden from St Petersburg, and while they could probably keep the swedes from taking the city they would likely lose Murmansk and if the Ottomans jump in later the Russians would be completely cut off from the West.
Russia was doomed either way, by late 1915 the seeds were all in place .. swedish involvement would have expidtited this. Access to Swedish ore, navy, and food would in my opinion A deciding factor.
if the swedes join and England doesn't the Italians won't join or at least not the for the French, then it looks like a gang rape of Russia I can't see the Brits staying out and letting France and Russia fall.
The movement in colonies being given up to the Germans, Italians and the renewed resurgence of the ottomans might cause massive heart failures in London