OK, let me answer that: it is No
Coaching as such was never necessary for any of the exams, whether it is IIT-JEE or design exams, so “NO” you don’t need any coaching but it requires discipline, you should be able to stick to a routine of 3-4 hours per day of aptitude and drawing practice. It totally depends on your hard work and practices. Without coaching, if you want to crack design exam then you need to be very careful about your preparations.
You will need a lot of practice about time management, increasing your speed of solving questions and improving accuracy to 95%. You will be fighting for 150 seats out of 12000 applicants for UCEED, 425 seats out of 21000 applicants for NID. If you are in open category the seats reduce to 40% (60 for UCEED, 170 for NID and 1400 of NIFT)
You will need a variety of practice like a drawing that requires imagination (imagine if gravity vanishes then draw a kitchen scene where food is cooking in 30 minutes) or find out 8 hidden objects form 80 jumbled objects in 3 minutes. You will need to master GK, English, Math, Logical and passages.
You will need to estimate your performance regularly by taking mock exams and evaluating your performance, if you can do it in a group the you will know your relative performance also.
You will also need a mentor who can course correct you regularly and motivate you as practice becomes boring especially if it is on for a year.
So, if you are confident that you can manage all above then you absolutely do not need coaching.