Is brain plasticity such that we can train ourself to see with our ears?
Short answer
Yes, we can see with our ears.

Background
Bach-y-Rita famously stated "We see with our brains, not our eyes". Bach-y-Rita worked for decades on sensory substitution. Sensory substitution approaches in general aim to replace for a lost sense by redirecting information normally captured by that sense to another still functional one.

Bach-y-Rita focused on substituting vision by tactile information. His Tactile Vision Substitution System (TVSS) captured camera images and translated them to tactile images projected onto the back of blind subjects. His decades of research eventually culminated in the commercially available BrainPort device (Stronks, 2016). 

Vision-to-auditory substitution devices have also been developed, most notably the vOICe by Peter Meijer and the prosthesis-substituting-vision-by-audition (PSVA) device, among others. The vOICe translates images into sounds by re-mapping their x-axis into the time domain, and their y-axis into the frequency domain (Meijer, 1992). This “image-sweepline” technique has subsequently been deployed in the EyeMusic device for use in sensory substitution (Abboud et al., 2014). The PSVA makes use of a pixel-by-pixel acoustic frequency transformation,where vertical position is coded as pitch and horizontal position as binaural intensity and phase differences, and brightness into loudness (Capelle et al., 1998).    

Peter Meijer refers to the vOICe as generating 'soundscapes', much like the approach you are describing. I seriously encourage you to contact him, he is a very nice guy and open to exchange. 

Anyway, to come to your question - can we see with our ears? Yes we can. Several studies have indicated that sounds can successfully be used to perform visual tasks, including localization (De Volder et al., 1999), pattern recognition (Arno et al.,2001a, 2001b) and depth-perception (Renier and DeVolder, 2010). 

Several studies have shown that the visually deprived brain is capable of re-routing auditory sensations into visual equivalents by re-routing this information to the de-afferented visual cortex in the blind (reviewed in, e.g., Poirier et al., 2007). This is referred to as cross-modal plasticity of the brain.  

However, the learning curve is quite steep, in that a lot of practice is needed to obtain useful information from visual information coded through sound (Stronks et al, 2015). Further, what is probably the biggest issue in analyzing soundscapes is visual clutter. While the visual system is very well capable of filtering out image clutter and extract the useful information, soundscapes will inevitably turn every irrelevant object in the scene into a corresponding sound. Front-end visual processing techniques are likely to be key to turning an auditory visual substitution device into a practically feasible device for the blind, or the sighted for that matter.  

The visual cortex is recruited for auditory tasks in the blind, but not in the sighted. However, I am inclined to believe it is practice, and not visual deprivation per se, that determines the performance with sensory substitution approaches in general (Stronks et al, 2015). 

References
- Abboud et al., Rest Neurol Neurosci (2014); 32: 247–57
- Arno et al., Neuroimage (2001a); 13(4): 632–45
- Arno et al., App Cog Psych (2001b); 15(5): 509–19
- Capelle et al., IEEE Trans Biomed Eng (1998); 45(10): 1279 - 93
- De Volder et al., Brain Res (1999); 826(1): 128–34
- Meijer, IEEE Trans Biomed Eng (1992); 39: 112–21
- Poirier et al., Neurosci Biobehav Rev (2007); 31(7): 1064–70
- Renier and De Volder, J Integr Neurosci (2010); 4(4): 489
- Stronks et al., Brain Res (2015); 1624: 140–52
- Stronks et al., Expert Rev Med Dev (2016); 13(10): 919-31