Those are two different points, I think:
- coal-dust firing was first used during the first part of the 19th century and from then on for the firings
of steam engines and turbines. So, the technology principally wasn't new and with enough R & D it may
have been possible to build a working propulsion system for an aircraft. "enough R & D" probably means
several years, especially if we consider the chronic lack of engineering capacity in Germany, not only during
the last years of WW II, but more or less from the resurrection of its aviation industry.
- Achieving a speed of more, than Mach 1 was uncharted territory back then, and the German designers,
including Lippisch had no solid results. But with enough R & D, it certainly could have been done, as the
development of the Convair delta wing aircraft may show. Those started from the work of Alexander Lippisch
and after about 4 years from the beginning, the sound barrier was broken, hardly and in a dive only ...
So, both points probably could have been achieved in a Germany during peacetime and without financial limits
and with no deadlines. Of course, it's quite unprobable, that such an aircraft would have been developed in
such a Germany at all ... :