Is it 'ok' to use a switched power supply to power a processor core?
Yes, it's done all the time.  True, switched supplies can produce more noise, but the efficiency improvement is usually enough of a reason to use them.  You just need to make sure you adequately filter that noise before feeding it to the processor.  

If your battery supply voltage is such that an LDO is still very efficient, then sure you can use an LDO and it will be a simpler, smaller, and less expensive design.  But usually that's not the case.

Also many people aren't comfortable with switcher designs and the necessary noise mitigation required, so they tend toward LDOs.  But if done properly a switchmode supply will be fine.  

You won't usually see max ripple specs on processor datasheets, but for 1.3V I would probably try to shoot for &lt;5% at full load.  If your component selection allows for that you shouldn't have a problem.

You mentioned it was battery operated but that the regulator would be powered from 3.3V.  So does that mean you already have a 3.3V regulator?  What is the battery type/voltage?