If I look at the Forwarder Management console of the Deployment Server, I'll find a summary of App Downloads in the last hour.
Is there any way to identify exactly which apps were downloaded, and by what clients?
Ah, this information is in the _internal index. The exact search will vary based on your version of Splunk, so you may have to play around with this a bit:
index=_internal component=DeployedApplication OR component= PackageDownloadRestHandler sourcetype=splunkd
| table _time log_level host app message