If replication is 600 seconds behind master will INSERT or UPDATE queries including `NOW()` be 600s different?
tl;dr No. 

The binlogs contain a set timestamp command before every transaction exactly to prevent this situation. This will only affect the session scope of the SQL thread so running queries meanwhile won't report date 600 seconds in the past.

To take a look you can run:

$ sudo mysqlbinlog --base64-output=DECODE-ROWS binlog.XXXXX |head -30

#150613  9:06:38 server id 1  end_log_pos 478584 CRC32 0xd86fcd7b   Query   thread_id=88627 exec_time=0 error_code=0
SET TIMESTAMP=1434179198/*!*/;
BEGIN
...