It isn't whether you could mow with a backhoe on, that would be an idiot move and likely impossible since it is usually either the 3 point hitch, or shared hydraulics, that raises and lowers the mower on many compact tractors. I also wouldn't leave the belly mower on while doing anything but mowing - though that ability seems to be a selling point on some models.
What I want to know, and am unable to go look at myself, is whether the BACKHOE FRAME allows the mower to be used. I do know that the loader frame is not an issue, that is easily found in online literature, but as for the backhoe frame ......... I even know what can be done on later model John Deere and Kubota models (mostly no)
Can't even find an example for sale that has a loader-backhoe-mower combo. So, my question remains.
BTW - I wouldn't even leave the loader on while mowing, though many do, and suffer from more rutting/scuffing from the front tires while turning.