For others who might have the same question (given the docs are not clear on this) i found the answer & it is as i expected.
Yes it does recover up to whatever WALs barman has last received starting from the backup time up to the current time.
Please see below console snippet for reference,
barman@4b412c1875cd:~$ date
Sat Aug 8 02:47:13 UTC 2020
barman@4b412c1875cd:~$ barman recover --target-time "2020-08-08 02:31:00+00:00" postgres-source-db 20200801T030001 /var/log/barman/TESTRESTOREFORTEST
Starting local restore for server postgres-source-db using backup 20200801T030001
Destination directory: /var/log/barman/TESTRESTOREFORTEST
Doing PITR. Recovery target time: '2020-08-08 02:31:00+00:00'
Copying the base backup.
Copying required WAL segments.
Generating recovery configuration
Identify dangerous settings in destination directory.
Recovery completed (start time: 2020-08-08 02:50:46.538480, elapsed time: 1 second)
Your PostgreSQL server has been successfully prepared for recovery!
barman@4b412c1875cd:~$
Thanks