Locks that are granted to your session can only potentially block other sessions, never your session (if blocked, you are always blocked by other session).

So, the answer is: no.

Join is used to find the rows needed to be updated and values to update to, but you always update single table.

Use sys.dm_tran_locks to view the locks granted to your session. After commit (or rollback) locks are released, so you might investigate locks inside explicit transaction, like this:

begin tran

update ...

select * from sys.dm_tran_locks

-- rollback