The metal detector is there for a reason - you are staying in one of the top ten targets in Jakarta, and probably the second hotel on that list after the JW Marriott.
JI historically doesn't do walk-ins though (the initial suicide vest attack before the vehicle bomb in the Bali attack being the only exception that springs to mind). But don't let the guards and the metal gate at the entry drive give you a false sense of security, take a look at the exit driveway - no guard, no gate - just a do not enter sign.
That said, if it weren't about twice as expensive as a lot of very nice four star hotels in Jakarta, I would stay at the GH without thinking twice about it.
If you want Hyatt at a lower price, the Aryaduta is run by Hyatt and is a nice place if you are in one of the recently renovated rooms. The downside is that the noise from the rooms currently being renovated will get you off to an early start on weekends and it is not attached to Plaza Indonesia as is the GH (which is handy for long stays as it gives you lots of dining options).
Have fun - I'll be back to Jakarta soon, but probably staying on the other side of the circle at the Mandarin.
TJ