My personal opinion, and having an innate spellcaster-turned-Spellsword myself...
Just because a spellcaster has an innage talent (i.e. Sorcerer or Bard) does not mean they cannot be taught to channel their gifts in a different way or improve them. I have GM-guided RP way in Connor's past that involved a lot of "wizardly" learning, though there never really was a mechanical benefit to it.
Anyway, this is going to boil down to what the CAs think of the existing RP and documentation as to whether or not a CDQ would be required, what shape that might take and so forth. There's no specific reason why a Sorcerer cannot be "taught" how to channel the talents of a Spellsword by a mentor. There's also no specific reason why a Sorcerer could not figure it out on his/her own. However, that said, there's other aspects to a Spellsword than just Imbue, such as the abatement of armor penalties to casting. I think the point there is that just because a caster is "innate" doesn't mean they automatically get anything that's magic just because. Even for innate casters, there's a process of "learning" magic, even if it's not book- and mentor-centric like a Wizard.
It is something that's going to be looked at on a PC-to-PC basis, as scifibarbie mentioned. The best answer to your question is going to come from the CA folks after a review of your particular situation.