I would like to add age as a predictor for my regression, but I would also like to make it a binary categorical predictor with a cutoff of 18 years of age.
I would like to do this because I suspect that age as a continuous predictor is loosely related to my dependent variable (I don't want to lose any information by eliminating it completely as a continuous variable), but there will be a much stronger categorical relationship.
People do often use binary categorical variables as 0/1 numeric variables in regression, yes. Note however you are almost certainly violating the i.i.d. gaussian assumption on regression errors in that case. But people still do it. An alternative is to learn two different regression models, one for people under 18 and one for people over 18. However this will reduce your data support, so if the number of data points for either group is too close to the number of remaining variables then that is not a good idea.