The TBI sub amp is a little different than most because each of the high-level inputs has a resistance of 300 ohms between them and to chassis ground so there is no chance that the negative terminals of the T-amp will short to each other or to ground. If you don't completely trust this you can always put a series capacitor in each line coming from the outputs of the amplifier that go to the high-level inputs of the sub amp. A film type is best, and should be somewhere between 100 uF and 200 uF -- with values near 100 uF you will start to roll off the sub-sonic frequencies, which could be a useful thing if you're getting rumble feedback from a turntable.
I ran the outputs of an original Sonic Impact T-amp directly into a Magellan 200su sub amp with no problem. I never tried it with my Clari-T, but it is basically the same thing as far as the sub amp issue goes.
I suspect that most sub amps are not like this, so if you own something other than a TBI, you should check with the amp manufacturer to make sure there is at least 300 ohms from each terminal to ground, and between themselves.
There is a link on Vinnie's web site which explains the benefits of SLA battery power.
Good luck,
Jim