Not directly, no. You'll have to re-create the query using the agg builder in Visualize - that is, the interface on the left side there.
Things like min_doc_count we don't offer controls for in the interface, but if you click the Advanced link at the bottom, it will expose a JSON input, which you can use to add that to the terms agg, like { "min_doc_count": 2 }
To see that you have a match, click the green play button at the top to run the aggregation, and consult the spy panel below the visualization. Opening it will expose a Request area, which will allow you to see the exact request that was made to Elasticsearch.
NOTE: You won't see a Debug option if you are running a released build of Kibana
Alternatively, you could get something close, and then save it. Then, go in to Setting > Objects > Visualizations, find the vis you just saved, and edit the aggs section under visState. This is sort of a last-ditch effort though, and can lead to you breaking the visualization and putting Kibana into a weird (but recoverable) state...