Server load question

Say you create a client proxy object SomeObject via a call to
Activator.GetObject, and then call a method on SomeObject.

Is there a live connection or other resource being kept in use on the
server for the whole time that SomeObject is still alive on the client
end? If you store SomeObject in a static variable or a class level
variable and don't dispose of it, but don't actually do any additional
calls on it, could that potentially result in an extra load on the
server?

Would there be any difference in this regard between whether the server
class was a Singleton or Single Call?

Not necessarily saying that I am looking to do this. Mostly just
curious.

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