It's entirely possible. Most non-governing monarchies still have themselves inserted into a position of power and simply rubber stamp the actions of the governing bodies. In the UK the Queen (or future King) has the ability to Veto a piece of legislation. Similarly in Canada, Australia and New Zealand the Governor General holds the veto amongst the other reserve powers.

However, the Japanese Emperor has no 'reserve' powers. So its ability to take power may be more restricted, however there's always a good chance that they would be restored to power in the event of an uprising.