No, In short, Domain authority is more concerned with backlinks to your website then traffic. In fact, if you are ranking for certain competitive keywords, it is likely that you have received several backlinks over a period of time which is helping you in SERPS.
Why not sign up for a free version of AHREF's and check the daily rise and fall of backlinks. AHREFS is excellent for this and u get a good view of where your site is going. If the backlinks drop significantly one day, then be ready for a drop in traffic next day. U will also realise the role of backlinks in SERPS.
Because i am in the business sector, i have seen some sites with pathetic boring articles ranking much higher then my very well explained articles. Just because these larger sites had higher number of backlinks because of the articles they churn daily and the backlinks they attract naturally.
All in all, your traffic will rise because of an increase in DA. But a rise in traffic does not increase DA.