Using T.T. ith out the battery..

no

Which model converter? Most don't need a battery.

If you have an older converter that needs the battery present, the worst that is going to happen is there is going to be ripple (an AC element) on the 12VDC line. This can result in some hum through the radio and if bad enough, some flickering of the lights.
It will NOT hurt the converter.

I do it all the time. At home my battery will be disconnected and still plugged in to shore power.

Some converters don't like operating without the battery. And if your towing it anywhere you'd also be giving up your breakaway capabilities.

In the "Old Days" prior to slides, I did it all the time. If you have slides, however, most state that a battery has to be hooked up.

Make sure the + battery cable ain't touching ground.