Some illuminated agents and publishers go for originality. For example, one of my favorite books ever is Breakfast of Champions, by Vonnegut, (4 stars on Goodreads, with 175,000 ratings) which has its own illustrations. (See below. Did I mention my very strange sense of humor?)
Another prime example could be Miss Peregrine’s home for peculiar children (3.8 stars on Goodreads, 490,000 ratings).
As a first time writer though it might be a bit harder to convince an agent/publisher to take risks given that you have not proven yourself yet.
Here is my advice to you: NEVER DULL YOUR PROJECT TO FIT THE TREND!
1-Write this novel as it is meant to be in your heart, with all of its quirks and oddities (and illustrations)
2a-Either go indie, publishing it yourself as is or
2b-Try first to publish a more classic novel to establish yourself. Once you have a relationship with an agent or publisher, discuss your experimental project.
Publishing is going to be incredibly hard, regardless of which path you choose. Don’t give up what makes your project unique.
I am assuming you want to do the illustrations yourself. If not, it might be perfectly reasonable to write the novel and propose it to agents/publishers suggesting illustrations be added by an artist of their choice.
Who am I to give you advice?
I am Gaia B Amman, the author of the Italian Saga (#TIS) a YA series taking place in Italy (4.8 stars on Amazon). Plan time to read it, because I am told it’s impossible to put it down ;)