Do the files exported in Export Management get uploaded into Oracle Content Server?

Yes, the exported files are available in Oracle Content Server in https://<POD_URL>/cs

You can find the content identifier in the ZCA_EXP_JOBS table in the column JOB_PARAMETERS (EXPORT_CONTENT_ID) as follows:

select JOB_PARAMETERS from ZCA_EXP_JOBS where EXPORT_JOB_ID=xxx;

JOB_PARAMETERS:

;LangIndHeader=NO;;REST_CON_NAME=null;TOTAL_SUCCESS_COUNT=xxx;EXPORT_CONTENT_ID=UCMFAxxxx;ERROR_CONTENT_ID=null;EXPORT_ATTACHED_DOC_ID=xxxxx;ERROR_ATTACHED_DOC_ID=null;