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CLUSTER Postgres relation on gist index

I am busy learning Postgres with the goal of migrating our current MySQL database to a Postgres/PostGIS spatial database.

We have a table containing (multi)polygons and do a large number of queries that need to find the properties within a given radius of a specific property. In MySQL I have Lat and Lon columns (in radians, of the property centroids) and use the great circle formula to do this.

I was reading about ways of improving performance in Postgres and came across a section titled "Cluster tables on specific indexes".

My question is: Does this work with spatial (gist) indexes to cluster the table by proximity of geometries?
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