Ah. To me, activities like this are almost an extension of adventuring - a Fighter spends a few weeks on the war's front lines or a Thief does some street work or whatever. Happens all the time in our games, usually if someone needs just a few more xp to bump.
Downtime activities - the type that might earn a few xp, anyway - to me represent things not necessarily directly related to one's class e.g. political activities and schmoozing, public works, research, donations or tithes, and so on. Non-xp-granting downtime activities include training, carousing, shopping, gear and equipment repair or upgrading, and so on.