Is it possible to perform clustering when short of free space on disk? According to v12 docs

Cluster with index scan requires


  free space on disk at least equal to the sum of the table size and the
  index sizes


and cluster with sequential scan and sort requires 


  as much as double the table size, plus the index sizes


Is there any way out if I do not have that much free space? i.e. can it be run in portions somehow?

If I run CLUSTER command and it fails because of insufficient free disk space will the performed work be entirely rolled back (when run with or without any parameter if it matters)?
yes postgresql would roll the transaction back.  

Almost all commands in Postgresql are run in transaction so if something goes wrong the command will be rolled back.

If the Postgresql system tables and WAL are on the same disk do not run this command if disk space is this limited.  Postgresql would panic and shutdown until space is freed up.

A Few things to keep in mind,  


Postgresql will not keep the table in that order so if the table is heavily updated. The physical sort order will be lost very quickly due to MVCC
Have to run the cluster command on a regular bases to keep the table's physical order which recreates the limited disk space problem. 
The advantage for clustering is for read only queries that select record set in the order of the cluster.


If disk space is limited and the table is updated/inserted regularly in a short period of time the table and indexes will grow to a point the cluster can not be rerun and vacuum will not be able run

looks like its time to start planning on adding disk space and moving these tables to new TableSpaces