I don't like them personally. I have never had a problem with ESD. Just make sure you touch the case before you touch anything inside. And make sure the computers unplugged. If its not then touching the case or using an ESD strap is worthless.
Computers have static electricity in them. If you are grounded then you can discharge that static and destroy system components. By touching the case unplugged you are not discharging static but your equalizing yourself with the components in the case.
In a situation like your ground device you have there you can become the ground if the components or case has a charge to it.
I had a big long post written up in reply to this but lost it all due to stupid adobe reader!!!
Basically it doesn't matter whether the case is plugged in or not when touching it for the purpose of "equalization" as you put it. Equalization and discharging of the static are the same thing. In both situations, static build up is traveling from the body of higher potential to a body of lower potential. You can still do a lot of damage to a device simply by touching it before grounding yourself. Static on the device is not a bad thing - it is the discharge that does the damage
The real protection is in the use of proper procedures and equipment. One of the key components in an esd strap is the >1 mega ohm resistor. This reduces any static discharge down to a trickle to avoid damage. The proper procedure is to ground oneself, then the device, then you can touch the device as both should now be at the same potential. If you are connected to the device and static builds up due to your movement then it will be at the same level on both you and the device and therefore avoid a discharge. If the connection is broken (which will nearly always happen) the large value resistor will reduce any discharge from you to a trickle and avoid damage to the device. The use of the grounding plug after initial grounding of you and the device simply provides an extra layer of protection.
A common mistake is to simply connect a wire from you to the earth connection of a socket. This is a bad move as you are now a very nice conduit for electricity to ground. The large value resistor also serves a safety purpose in this case by encouraging any dangerous discharge to take a different path. For this reason, once i have used the grounding plug initially, i prefer to disconnect from it to remove this possibility.