Do they gain experience?

[Q]

Ships are usually parked in orbit around a colony with a resupply facility. So if you include the training facilities on resupply colonies you will have increased chances they will be effective. However you must make sure that the AI builds a resupply colony first in every system and not (as usually the case) a mining colony with a resupply facility!
Another possibility would be the introduction of combined resupply/training facilities (which need the corresponding tech levels for the training facilities). If you give them a higher roman number and place them directly under the normal resupply facility in the facility text file the AI should use them instead of the normal resupply facility.