Can a NEMA 6-15p plug into a NEMA 6-30r?
No.  The backwards compatability of 20A sockets with 15A plugs is a "one-off" because of a very special exception in Code.   

It does not apply to any other combination of ampacities at any level.  

Generally you want the breaker to be a reasonable near match to the appliance, so if the appliance has an internal problem, the breaker will trip before the appliance's line cord starts a fire.   30A is just too large to protect a common appliance cord.