Unless a device has the capability to sample audio 2.8 million times a second (5.6 for "Hi def" version), Then No.
This requires a pretty specialized chip and/Including an extremely accurate Clock and ADC voltage/PSU to have a noticable advantage over common methods. Wikipedia "Direct Stream Digital" has a link to NativeDSD Database (by nativedsd.com), but it's play orientated, not record. I only looked at the Sony entries (since they championed the format) and no phones there. I'm sure a phone app could produce a DSD file, but it would be converted PCM for sure.