As already mentioned the only way disciples gain experience, other than combat, is by having the Potency promotion given to Spiritual disciples. This is a rather slow and erratic process but not that different from the slow rate that adepts gain free xps. I'm not sure of the exact chances now, since there have been many changes, but in the old FFH2 manual Channelling 1 has a 20% chance to gain 1 xp per turn and Potency also has a 20% chance.
There are several great tricks that a Spiritual leader can play by building several of the level 1 disciples and letting them gain xps before upgrading them on their alternative upgrade path, rather than simply upgrading to the priest of that religion. The upgrade to priest requires that you adopt that religion, not a big problem for a Spiritual leader unless you have religious heroes you want to keep, but the alternative path doesn't need the religion in some cases.
A superior mage can be made by building a Spiritual savant. The unit gets a free potency, mobility and medic promotion and when it has grown to 10 xps can be upgraded to a mage. If you have at least 3 sources of any mana type it immediately picks up the free level 2 spells and level 1 from any 2 sources of mana. You now have a mage with Channelling 2 and Potency promotions that gains xps much faster than an ordinary mage upgraded through the normal adept route. It also has a free mobility and medic promotion and so will be better promoted than most other mages with the same xp. It does miss the chance to pick up the free level 1 spells that an adept gets on creation. To build these savants you only need get the Corruption of Spirit tech and build an Ashen Veil temple, no need to adopt the religion and become evil. And you only need 1 city with the temple so it won't push the Armageddon counter up much, if that's a worry.
A superior ranger can be made by upgrading a Spiritual disciple of leaves. If you wait until it has gained 5 xp it can immediately take the combat1 and subdue animal promotion on upgrade to ranger. This ranger also has a free mobility and medic1 which is very useful when he's out capturing animals for you.
A slightly superior Stygian Guard can be made by upgrading from the Spiritual Zealot. This can gain xp while sitting around as a level 1 and can be built with only an OO temple and not adopting the religion. However to upgrade to either the Stygian Guard or the Cultist the religion is needed. Perhaps the biggest advantage of this route is that you can recruit the Zealots many turns before researching the Fanaticism tech and then have a large number of well promoted Stygian Guards when you reach this tech and adopt OO. A similar trick can be done for superior Crusader and Paramanders but these are seldom the main troops or have the impact that Stygian Guards have.
So next time you have a Spiritual leader consider playing around with these religions and their level 1 disciple. In fact since you're Spiritual you can do all of these tricks in the same game
