Would I have access to referenced logs related to Rapid7 in my cloud instance or would I have to reach out to Splunk support?
Access to splunkd.log is available to anyone whose role gives them access to the _internal index. The TA's logs should be in the same index.
If you don't have access, contact your Splunk Admin.
That's right, if you have the sc_admin role on Splunk, you should be able to read the logs:
index=_internal source=*splunkd.log*
index=_internal source=*ta_rapid7_insightvm_insightvm_asset_import*
If you are not a Splunk admin, then ask a Splunk Admin in your team.