Maybe the main benefit illustrations can give you is helping your marketing. This is a way to distinguish from competition, help users to recognize and remember your product. An illustration is a visual language your app speaks to the customers, builds trust, establishes an emotional connection.
The success will depend on the quality of your customer research. You should figure out user's background and preferencies, choose the style of illustrations that fits user's mental model. And of course draw them perfectly.
Guys from Intercom
(multichannel communication platform) changed their visual style about 3 years ago.They made dosens of illustrations with funny characters-animals who play roles of customers and managers and showed how it's easy for them to communicate inside the product.