Noticed that I could upgrade Swordsmen with several City Raider promotions to Riflemen/Infantry. Having strength 14/20 guys with +75% city attack comes in handy before you get tanks.

Did not use it in my GOTM, but in retrospect, maybe I should have. Normally I play on as high science rate as possible and usually find it better to build new than upgrade existing units. This could change that a little.

Would this be an exploit/bug? Could be reported elsewhere, I haven't searched thoroughly...

Nope, not an exploit, just a smart move. Upgrading old units as a opposed to just building new ones is a strategic decision; when the old units have experience, it's often better to upgrade. Especially in a situation where the promotions that unit has aren't available to the new units...

You only keep 10 experience points though when upgrading.

It was the promotions-not-available that had me wondering. Will be a new strategy for me, getting some City Raider III's just for upgrading.

And even though you keep only 10 XP, you still keep all promo's if the units were higher than lvl 4. Just lots of XPs needed until unit gets next upgarde.

similarly you can get gunship with medic bonus, by upgrading mounted units like cavalry.

Yes I use this in all my games. Get Theocracy and Vassalage going early and then later on in the game you should have at least a few powerful units to upgrade while still using more modern civics. My favorite is Infintry with Drill III.