I think an
FAQ clarified that you can do this.
While technically only applicable for Death Guard, I can see it being applied generally and not having too many complaints.
Q: If my army is led by a Chaos Space Marines Warlord, and I have a Detachment of Death Guard, can I use the Gifts of Decay Death Guard Stratagem to include a Relic on a Death Guard Character?
A: Yes. The only requirement to have access to Stratagems is that you have a Detachment of the appropriate Faction. If you have a Death Guard Detachment, you have access to their Stratagems.