Yes, this will work, subject to stability and startup concerns.
Let's do some sums. Say the buck converter is supplying 10 watts. It will need to consume (say) 11 watts. The boost converter, with an input of 10 watts can only produce 9 watts. This leaves the external power source to inject an extra 2 watts, to cover the losses in both converters.
Stability is a real concern, as (assuming a bench power supply) you have three connected systems all with feedback loops controlling them. There is every possibility that they could fight each other, leading to wild and possibly damaging swings of voltage and current.
Ideally the power source should be something unimpeachable, like a lead acid battery, with a very low impedance, capable of sourcing and sinking large currents. Use a current-output battery charger to keep it topped up. An alternative would be a very large capacitor, providing a low impedance, and an ability to source and sink current, with tame behaviour.
The boost converter should be current output. Its output voltage will then be defined by the power source. The buck converter will then consume all the current the boost converter produces, with the extra current to cover losses being drawn from the power supply.
Startup may be an issue if the converters have problem into zero load, or have large input storage capacitors which allow them to momentarily draw less input power than they are providing. Ideally, you would start with the boost converter set to zero output current. The buck converter will then be drawing its quiescent current, plus an input for the boost converter's quiescent current. As you increase the programmed boost converter output current, it will throw more load onto the buck. It may help stability if you have a small real load on the buck output, just to increase the current required at 'no load'.