I'm looking to see if there's a possibility to search specific data from a specific address, such as the population in a three mile radius.
Normally in ARCGIS, I would need to enter the address, create a circular buffer of 3 miles, and then enrich that data layer to extract population information.
Since I am only interested in the population number, would it be possible to query this search through an API and get the returned number?
Not an API query solution, but here's a workflow in ArcGIS Online's Map Viewer Classic that may be slightly simpler than what you were suggesting.
1. Open a map, and use the address search in the top right to find the address of interest.
2. In the Search result pop-up, click Add to Map Notes to make a temporary feature at that point.
3. Go to Analysis > Data Enrichment > Enrich Layer, and set your input layer as your new Map Notes layer
4. Select your desired population variables, and then define your enrichment area using a Line distance of 3 miles (No need to create a buffer ahead of time!)
If you have network analysis privileges, you could even define this area to enrich based on travel modes such as a driving time or walking distance if you were interested in leveraging the road networks