The 12V socket in the boot is only rated for 25AMPS according to the manual - I doubt your amp will run off that.
Even if it does it's likely to either blow the fuse as soon as you push it or overheat the wiring and set fire to something.
The most likely scenario though is exactly what you are describing - the Amp just won't power on.
You can use it for the remote line to tell the Amp to switch on but it's still not recommended as most cars generate and audible POP through the Sub if they are activated by the accessories switch instead of a remote-on signal from the head unit.
I used an
LOC with "signal detect" which has a remote line for the Amp that it activates when it gets sound from the speakers - works brilliantly. (cost me $35AUD for that unit so about £20 UK?)
-H