That depends a lot on the capabilities of the device. Sapling is primarily designed to support isolation of spend authority in very small devices (in theory a few hundred bytes of RAM, and very little computational power, is sufficient). As the spec says, in that case privacy is lost to whatever party/device is doing the zk-SNARK proving. However, the proving itself is much more efficient in both time and memory for Sapling – so, it’s entirely plausible that a mobile phone or other small/dedicated device can do the whole spending process without loss of privacy to any other party. For that the device wouldn’t necessarily need to be a full node.
We don’t know yet what the timescale will be for support of shielded transactions on mobile.