Also, see this tank experiment (link below). As far as I can tell, in those pumping and suction experiments the water has uniform density and there is no specific site of dense water formation, yet overturning does occur.

http://weathertank.mit.edu/links/projects/ekman-pumping-suction-introduction

Ekman suction and tidal mixing are independent of deep water formation rates. Deep water formation by surface buoyancy forcing at high latitudes is not the only way that abyssal waters can be renewed. A thought experiment: an isothermal isohaline ocean is subjected to ekman pumping from surface wind stress in one region. Upwelled water would subsequently redistribute away. Conservation of volume dictates that the upwelled waters are replaced, and of course they are by surrounding waters at depth, possibly many depths. An overturning circulation will become established, with waters away from the upwelling site "sinking" to replace the upwelled waters, although the sinking is more akin to falling, as there is a decrease in the volume of waters below. Possibly the sinking would occur uniformly over the entire non-upwelling basin, or it might be confined to an area around to upwelling, but the resulting overturning circulation would look different than our current MOC.

The rate of surface water transformation depends only on local buoyancy forcing and initial seawater properties, it doesn't know about remote upwelling rates. However, if upwelling ceases, the abyss would eventually fill up with dense transformed water and the rising isopycnal of that "deep water" would eventually limit the depth to which the newly formed dense water sinks. So, in that sense, the rate of deep water formation does eventually depend on there being upwelling or tidal mixing elsewhere.

Wouldn't one expect local Ekman pumping (wind induced upwelling) and internal tidal mixing to be indifferent to the rate of remote deep water formation? The properties of the upwelled deep waters certainly vary based on what their surface properties when they descended.

I can't speak for other ocean or climate models, bit geothermal heating is included in NASA's ECCO ocean models and state estimates. Its magnitude is small relative to ocean surface heat fluxes but geothermal heating does help maintain a more realistic deep ocean state by reducing the drift in deep temperatures.