I'm going to assume yes. I was deliberately avoiding Smithing in my revent game because I felt it was going to obsolete my Praetorians, so I wanted to get as many of those lovely free promotions as I could so I could upgrade them later before the end of their era.
Well, it said I had around 16 turns to research it. After my conquest of Ethopia - of which almost every city claimed "You learned some of the secrets of Smithing" it said I could research it in one turn.
A while back, we put in extra unit upgrade paths to most UU's with free promotions just to allow you to build them longer. Praetorians and Jaguars upgrade to Swordsmen OR Heavy Swordsmen specifically so that you can build them until you get Armor Crafting; once you get Smithing, you can still build your Light Swordsman-class UU and immediately upgrade it to Swordsman, keeping its free promos. I was just wondering if you knew that.