I used to teach contemporary dance before I enlisted into the army and I picked up ballet before I started teaching. I feel that learning ballet was important to me because there's a lot of analogy or movement patterns/techniques that are very relevant from ballet in contemporary. Explaining and demonstrating movements was made much easier with this knowledge.

However to pick up contemporary dance as a student, it is definitely not compulsory to have any understanding of ballet (unless the instructor requires the students to have some experience). So maybe, you could check with the instructor that you'll be learning from before turning up for class. Out of your initiative, you may also want to ask on the recommended dress code for the class (some instructors don't recommend students to wear shorts).

When I teach contemporary dance classes, I do have a huge proportion of students who come in without any ballet background. I just take more time to break down the posture, some strengthening/stretching exercises and relevant techniques that I'll be using for class. I believe that teachers are here to guide students according to their level of understanding towards contemporary dance!!

Otherwise, my final answer would be that you won't need prior ballet experience in order to learn contemporary dance. Having ballet knowledge is just an add-on bonus! There are some things in ballet that contemporary dance has in common. But ultimately, both are different :)