Mark 6:13 and James 5:14 use aleiphô in a similar therapeutic context (in other contexts, Matthew 6:17; Mark 16:1; Luke 7:38,46; John 11:2; 12:3), but I fail to see the relation with spitting. And the Greek NT word for "poor" is ptôchos, unrelated to ptuô as far as I know (except on the grounds of random vicinity in alphabetical order, which could as well bring ptôma, "corpse", or ptôsis, "fall", into the picture...). So I still think the Markan occurrences testify only to magical practice, with little theological overtones if any.
However, unsurprisingly, the Johannine occurrence fits the Gnostic symbolical paradigm. With such evocative terms as "mud", pèlos, typical of the "potter" creation motif in Isaiah 45:9 etc.; Job 10:9; 33:6; 38:14 (cf. Genesis 2:7, other LXX Greek term) and "anointing", epichriô, related to chrisma/christos.