In theory. However, not likely, due to the damage from nuclear war.

For example, had a nasty storm here and I lost internet for 3 days while they fixed.

There are no repair techs operating in FO.

Their network was between Fallout shelters and even nuclear powerplants.. .I have a feeling that Posiedo-Net was not consumer a grade network; it also worked just fine in the games ~over a century and a half later. The Enclave had no trouble connecting to Gecko, or to Vault 13.

I wouldn't say it is fine. The menu to access different places was limited, with at least one that was completely offline, Cheyenne Mountain if memory serves was one.

We also should assume, at least I do, that the Enclave did work to restore the system in the region, but again that would be limited. This was all talked about in a Bible.

Logically, nothing would work. In game world things work when needed, plot devices. 200 years later there shouldn't be any working satellites, heck, should there even be a vast sat network anyway without microtransitors.

Who said anything about satellites? (And why would they lack microtransistors? The setting is one of 50's aesthetics, not 50's limitations. It reflects what will be popular and useful. Tubes for instance are less affected by radiation than transistors ~but that doesn't mean they would not use them, just that they are less popular.)

**And for those that refuse to believe anything in Fallout can exist if it didn't exist in the 50's... despite plasma and laser rifles being in the games... Transistors were invented in the mid 50's.

Part of the 50's aesthetic is 'built to last'.