We recently sold a 1999 Allegro and it never had an inverter, which is not unusual for gas coaches of that size (32 feet). Our house battery-bank consisted of two 85 AH batteries, which, in my opinion, were not big enough for all but the smallest of inverters. It wouldn't be difficult to install one. The simplest can be had for about $40.00 and simply plug into a cigarette lighter but, other than small devices, they don't power much - chargers, very small TVs etc. Others are hard-wired and can power larger appliances.
Inverters should be sized to your battery-bank. If they're too large in relation to the battery-bank, they can drain the batteries quickly - especially if they're used to power larger appliances, or even smaller appliances for long periods of time.
Kev