The protocol states that it will upload the Diagnosis Keys, a set of Daily Tracing Keys relevant to your exposure. So in short, if this is the case it forces the user to either upload all their keys or none.
I would like to note that a v1.1 has recently been released, my information is about v1.0.
The specification (at least v1.1) contains nothing about uploading keys. The API appears to provide only the minimum required for protocol implementation.
The ENSelfExposureInfoRequest class can be used by an app to obtain diagnosis keys for the previous 14 days. What an app does with those keys is up to whoever implements it.
I would like to note that a v1.1 has recently been released, my information is about v1.0.