Long story short, I have a routine to turn on certain appliances in my house. I would like for this routine to proceed only after it has detected my voice profile. Is this even a possibility? I have looked around to see if Alexa has this ability but I can find no info on this anywhere in the app or online. Would it be possible to do this without the need to make a skill? Any help would be appreciated.
Yes, this is possible but it will take some work and a custom skill. First you need to setup your skill to support Personalization. See here https://developer.amazon.com/en-US/docs/alexa/custom-skills/add-personalization-to-your-skill.html
Each intent request comes with a unique user id that identifies the owner of the device. If the skill is personalized, the request will also come with a Person object that gives an id for the recognized person. You can look for the personId and if it matches your person then you launch your action.
This link (on the same page as above) describes the person object. https://developer.amazon.com/en-US/docs/alexa/custom-skills/add-personalization-to-your-skill.html