Got a multimeter?

The fact that it is battery-powered suggests that it's current draw isn't too great..If you know the capacity of the battery, and how long the battery lasts, then you can calculate it's current usage:

current (A) = capacity (in Ah) /battery life (seconds)

Now the type of voltage regulator in the 12V circuit will affect the current drawn under 12V. If the regulator is linear, then the 12V current will be similar to the above result. But this is inefficient - for a 5V device, 7/12 of the energy is disippated as heat, so either the unit of the adaptor will be noticeably warm if that is the case.

If the regulator is switching, then the 12V current is going to be lower than the battery current. eg, for a 5V unit, we only need 5/12 of the battery current to get the same power.

The amp remote is capable of driving 1A IIRC, so you should be fine. But before you hardwire your expensive GPS to it, make sure that the 12V regulation circuit is acutally internal, and not part of the adapter!