I don't think so Garry, the US would have invaded Alaska. I don't think Japan would have been able to defend it. How would Japan be able to defend against a possible 30,000 US troop invasion force during WWII?
You are ignoring a few things... first of all the Europeans celebrated the Japanese victory against Tsarist Russia, the Japanese got a lot of assistance from Germany and other European powers with their navy, and the Russians were the bad guys even then, so a Japanese invasion and occupation of Alaska would probably be supported by the west in general... remember the US didn't see it as American territory then.
Also come the 1930s and Japan would be able to satisfy most of its energy and mineral needs from Alaskan territory... remember in the real world their first choice was to try to take Siberia and they were stopped by the Soviets in Mongolia. After that they had to revise their plans and instead of heading north and west they headed south for oil and resources.
Alaska would not have been heavily defended by the Russians and would probably have been easier to invade and occupy than China was.
With no lease or sale to the US, the US would have no claim to that particular piece of land.
With Japanese occupation there would be no reason for Japan to attack Russia, nor to invade the rest of the Asian Pacific region for resources, so WWII would have been a strictly European affair.
With no combat in the Pacific there would be no reason for WWII to end with US troops in Japan. The Korean war would not have happened and Japan would likely still occupy Manchuria and China and Korea, as well as Alaska.
Japan had some very mediocre weapons and equipment during WWII, their tanks and hand guns were dire, but their carrier aircraft were rather good and a few of their other aircraft types were impressive too... though some relied on German engine technology...
Long story short Japan might have stayed out of the wider war, attempting to preserve their empire in Korea and keeping their invasion to just China... which probably wouldn't work out well for them in the end anyway but it would take a lot longer.
Obviously no one can say for certain, but I would think eventually those Koreans and Chinese would get sick of Japanese occupation and try to do something about it.
With some countries a good hard slap... like two nuclear explosions... can wake a country up and make it focus and set it on a better path, but in the case of Japan they don't even mention it was the Americans that nuked them because they are so Stockholm syndromed over the US they can't help themselves.
It is ironic that such strong colonial powers like Japan and the UK and others will fall in line to the big alpha male on the block... but that alpha male has to win all its fights and prove itself all the time or they will turn on it and fight amongst themselves to take the crown...
When the US dollar collapses it is going to be internal fighting in the US and amongst HATO allies that will be the real issue... they will understand attacking China or Russia or both would be suicide and I don't think they are actually interested in that.