Input filter on DC-DC converter when it is the only load on a source?
would you still get some benefit in terms of cleanliness on the output
of the buck converter by having the input filter?

You would get reduced EMI and that could make a whole heap of difference if it allows your circuit//module/system to pass EMC regulations. If your battery has wires feeding your circuit then even more so because you don't want the battery and battery wires acting as a loop antenna and emitting any significant level of switching noise.
Even if you don't have wires (or the wires are very short), there is a still a loop formed because your battery has a large physical size compared to most other electronic components.
It is advantageous to use a shielded inductor and one that is self-resonant at a frequency (SRF) at least ten times (or more) than that of the buck switching frequency. Having said that, using one that isn't can be supplemented by a smaller value inductor in series that does have a high SRF. Sometimes it's a good idea to model these components and ascertain their net effect. Sometimes it's even beneficial to force the smaller inductor to self resonate at a frequency below its SRF in order to minimize EMI.
All tricks of the trade.