No, paid ads will not affect your organic performance or engagement on Instagram. Organic posts are often slower to reach business goals, and while it's free, it takes a lot of time, experimentation and/or experience to get right.
Paid advertising will help supercharge your marketing efforts and help connect with new customers or audience members. Reach a larger number of people, target your ideal customer more precisely and hit your business goals faster with paid advertising. Increase your brand awareness, profile engagement and acquire new followers you would not be able to obtain with organic.
The foundation of the majority of integrated social media strategies utilise organic to serve and delight your existing customers, while attracting new prospects with paid ads.