Does DBCC SHRINKDATABASE free physical disk space during its run? I want to run exactly this command:
DBCC SHRINKDATABASE mydb

When I run this just for a while and then kill it, will the physical database file be a little bit smaller?
In other words: Does the command immediatedly free physical disk space during its run, or does it first a full reorganization, and only then free all physical space?
EDIT: We have simple recovery model, so our log file is very small and we only have one big database file.
DBCC SHRINKDATABASE does not rollback when the process is killed so theoretically you'd be able to run it for a period of a time, kill the process, and have some reclaimed space (assuming there is any that can be reclaimed). See this for more information.
Also please see and research the warnings I provided against shrinking in my answer to your other StackExchange question.

...[it's] heavy operations, generally nonsensical to do because if
they grew to a certain size they'll likely grow back to that size soon
anyway and a growth operation is also heavy, and shrinking any
database files (except Temporary) does have a small risk of data
corruption.