Your outlined method should be successful (as long as you append the March NBER files in order by year). However, it is important to understand that the March supplement and March basic monthly samples cannot be merged due to the March over-sample (as mentioned in the first and second answers to this question). Because the NBER method for linking individuals was developed for matching persons across years (rather than months) you will encounter a number of new technical issues not addressed in their methods. I highly recommend reading through some of the articles that have written on Longitudinal Matching in the CPS.
I hope this helps.