I've setup a Batman mesh system with one router and 5 access points. Two of my access points have wired connection to the router so I've setup the mesh interconnect there over a wired connection. Should I still enable the wireless mesh interconnect to provide other access points that are further away from the router a wireless path through these wired points?
If you have the opportunity for a wired backhaul, use it - and if you use it, there's no point for a second wireless backhaul. A wired connection is always faster, more reliable, supports VLANs and is easier to deal with, it makes no sense to add a less reliable/ slower wireless link in parallel, which will only cause you grief (looping) and may mask issues with the wired uplink.
Whether this works well all depends on the physical locations/layout of the mesh nodes.
As @slh says, mesh bridge looping is likely and is potentially a show-stopping problem.
Both batman-adv and mesh11sd mesh backhauls can mitigate mesh bridge looping. I can't remember if batman has this enabled by default, but mesh11sd does.
Note: STP does not help by itself as the looping will be at mesh interface level, not at bridge level so something more is needed.
I also fail to find a source about the default but IIRC it's enabled by default.