Is it possible for me to install Splunk Enterprise for a couple of days and play with AD integration and DB Connect to a postgres database?
You can use Splunk trial version for most of the POC activity but some enterprise features will be disabled. You can play with DB connect App or any other app but cannot use AD/Clustering/Distributed search and others pointed out in Admin manual.
Yes, when you download and install Splunk Enterprise, you get a 60-day trial license that includes all features and allows you to index up to 500MB a day. After the 60 days, it converts to a free license. You can continue to use the software at that point, but it has a few limitations.
See Splunk Enterprise license lifecycle(s) in the Admin Manual.