Well, this might butterfly the Russian Revolution and Cold War altogether. If gold is ever discovered, you might see boom in settlement, but I doubt it would be Russian settlement- the US and Canada are closer with more people. This would probably lead to a situation similar to what happened in Texas-Russian Alaska had only 700 settlers in 1867. Alaska would either be likely to be absorbed by the US or Canada(or partitioned between the two) then, or if the Revolution hits, it would be brought into the fold then.
Filibustering actually didn't have all that great a track record.
The Russian Empire was not Mexico. It had gone toe to toe with Napoleon, helped to Crush France during the revolutionary wars, beaten the Swedish Empire, dismembered Poland, kicked around the Ottoman's like a rented mule, conquered Siberia, overrun central Asia, bitten off pieces of China, and fought France and England to a standstill recently.
If there was big money to be made off a gold rush in Alaska, the Russians would send in enough troops to put a lid on it, they wouldn't be gentle, and they'd settle it.
They surely will not give up on a valuable territory. They sold Alaska because it was worthless to them, not worth the effort of holding onto it. If it's valuable, they'll fight to hold onto it.
Not saying that they'd succeed. But while the territory is somewhat more accessible from British Colombia, or from the Pacific, or the ports on the American West coast than it was from Russia, it wasn't really super accessible to anyone. Alaska really was the ass end of the world. British Colombia was a minor settler colony in the British Empire, it wasn't a major staging post, so the British Navy would have had to sail literally around the Atlantic or Indian Oceans, through the Pacific to get there. California was a state, but not the huge state it was now, and there was a lot of emptiness between. The American west and west coast was still developing.
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