Questionable.
There’s about 60km between modern day Russia and Alaska, and plenty of troops are already stationed (and were at the time) on its eastern border. Alaska would provide a lot of resources, and it could absolutely be guarded.
But, at the time, Alaska was seen as nothing but barren piece of cold land, not really useful for anything.
Vladivostok is barely the closest populated Russian area. Even among major cities, Petropavlovsk-Kamchatsky is significantly closer, not to mention Anadyr and other smaller ones. Besides, if Alaska would remain Russian, you bet there would be more connections. They just don’t make much sense in the current realities.
Russia has the technologies and infrastructure for efficient resource extraction under extreme conditions, and some of those resources (for example, nickel) are primarily located inside the Arctic circle. Moreover, under American leadership Alaska has still been one of the resource extraction hubs, with up to 2 million barrels of oil produced per day at peak, and about 500 thousand currently, 17 metric tons of gold currently produced per year (and expected to grow), etc. etc.