The US Navy's Mercy class hospital ships are not. Not sure about any others.
And Kaiser's right. This is a fine ship indeed. Having a cargo pod converted as secondary hull of a starship actually makes perfect sense within the Trek universe, as they offer a lot of internal space. (The US Navy's Mercy class are converted supertankers) Hell, I've seen fan-designed cargo-pods with impulse drive and even with a single warp nacelle sticking out underneath, essentially making them instant starships, so why not combine one with a dreadnought saucer as you've done?
And while they are certainly not in the same league with such ships as the Saladin/Hermes or Constitution classes, they are
beautiful in their own right.
EDIT: @ B.J.: I didn't find anything about even defensive weaponry on Wikipedia's page on the Mercy class the last time I looked.
Nevertheless, for a Trel hospital ship phasers should be fine. The Feds probably don't have interstellar treaties covering such issues as shooting at hospital ships with EVER ONE of their neighbours, hence requiring them to be armed at least lightly, just in case. (Not that their neighbours would neccessarily care whether or not they are commiting war crimes.)