I don't think there'd be any point mixing lightly cooked white sugar (demerara) with uncooked white sugar.
If you want to approximate brown sugar you'll need to add molasses to white sugar.
white sugar + molasses = brown sugar
white sugar + heat = demerara sugar (which happens to be brown in color)
I've never done DIY yeast, but if you're trying to follow a recipe that calls for brown sugar and can't find it, you could follow
these instructions to make it out of white sugar and molasses.
Cooking (or caramelizing) white sugar will make sugar brown
in color, but it won't make
brown sugar. To do that you need molasses, not heat.