I highly doubt it, not if they remain isolated after going full far rightHowever, no matter how crazy things will get in the US, imo they will always remain far ahead of the USSR economically and technologically
America's economy is strong, the strongest even, but thats because it has the whole world as its market
It simply wont surpass the USSR(which was already the Top 2 IOTL despite all its inefficiences and crap done to it by the now butterflied away OTL rulers) if it becomes a giant North Korea, no matter how fertile the soil is or how educated the now nazified population are
Going full militaristic wont also make them more powerful in the world stage, not really when your enemy can nuke you at any time they want and if you get yours MAD becomes the rule
Fact is that while not militaristic IOTL the US already had the most powerful army in the world and that wasnt what won it the Cold War, the existence of MAD made the use of such army directly against the USSR and in this case being even more militaristic would only mean wasting more money with an already massive and strenous military power that they simply cant use - not without getting nuked
Rather militarism would make the already damaged american economy weaker due to the strain of funding a large army imposes on all sectors, having all citizens conscribed alone would create problems and any technological advancement that the US would otherwise have would instead be focused on improving said military
Dont expect any of the great inovations from the capitalist society of the OTL US in this Fascist one, and unless the soviets challenge them to yet another space dick measuring contest(which would be yet another pointless strain as the OTL USSR already got to Space first and in this scenario it'd be perfectly capable of reaching the Moon) there wont be any of the fun toys we got from NASA thanks to the discoveries made by their engineers