Vaccuum tubes are a lot more resistant to effects of EMPs than later circuits. About ten million times harder than integrated circuitry than that used even in the 1970s.
As Carl noted though it knocked out Japanese radio and telegraph for quite a while and (IIRC it's been years since I've seen the stuff on this) while the tubes themselves weren't actually damaged there was arcing and other damage (good old "arcing-and-sparking" ) throughout the system. Sure it was simple as replacing a fuse here and there but you have to find the fuse and quite often that's not where you start looking nor quite as obvious as that. Keep in mind the US didn't even really begin to understand EMP issues till the mid-50s.
Radiation wasn't also well understood at this period. Keep in mind the U.S. also planned to use atomic bombs in Japan during Operation Downfall, meaning American troops and marines would be exposed to deadly fall out while fighting the IJA.
The sad part is it's unlikely they'd have actually 'noticed' for decades given how the assumption was that both the Allies and Japan would resort to heavy chemical use and the troops and civilians would be dealing with a heavy aftermath of that which could hide the radiation problems for decades. Let's remember in context that the A-bombs in this case are simply another "tool" in the box and any studies of the aftermath are likely (specifically in Japan) going to be hindered by a very hostile population as well as hostile conditions. Using them in Europe would probably have more near-term effects and indicators but you'd have almost every single Allied and ex-Axis government not wanting those results to be public knowledge.