I have an LCD TV on Playtime that came with a 240 AC to 12V DC power supply ‘brick’.

I quickly reached the same conclusion that driving it through an inverter was unnecessary and made up a new cable to supply the TV direct from 12V; it works fine with no problems.

As suggested above, you should check that the TV will be OK to work at up to 14.4V (if you will ever run the TV while charging – shore power or engine) but I suspect, like mine, that it will be OK.