There is a chinese transceiver the X1M, look at x1m.wikia.com and on google. That is basically an SDR but no one has worked to build open firmware for it yet. i think we have a great chance to build something awesome from a cheap and solid chinese clone.
Can we? Maybe. Will we? Unlikely.
There are a number of things that need to happen to pull it off. First, we have to figure out just how thoroughly they might have locked it down to prevent just that. While it seems unlikely that they went to great lengths, you never know.
It's also possible that the infrastructure to reprogram it on the fly isn't totally functional, which would make it difficult for the average ham to make use of the new firmware.
Another issue on this front is available hardware. If the internal hardware is fundamentally handicapped, and reports regarding CW performance and signal quality suggests it might be, then even new firmware may not be able to fix the real problems.
A bigger impediment may be the community that builds up around it, or more precisely, the lack of it. A good development effort usually requires a core group of capable programmers, and the community support to make it worth their time and test the firmware. Given the somewhat concerning reports of poor signal quality and lackluster hardware, it may be hard to drum up that kind of community support.
This is the first shot across the bow though. More radios like it will come. It's an inevitable economic result of the inflated equipment prices you see on the market.
We can, but it's not likely to happen.
It wold take a considerable effort from capable developers to write it. First of all it will be needed to get access to one of those equipments, than a lot of other stuff had to be done.
Honestly I dont think it will be done soon, since there are allready plenty of alternative firmwares for other radios.