I'm not sure whether your sentence is grammatically correct, but it would be better to say: "He experiences a complicated love affair."
His book is also notable for the small glimpses of a deeper, pre-mythic, reality he lets slip - like Dodgson's passion for Swinburne's sensual and 'scandalous' poetry - and for the fact that, alone of any biographer until the modern day, he admitted - or at least implied strongly - that Dodgson had experienced an unhappy love affair.
During a stay in revolutionary France, Wordsworth had experienced a passionate love affair and fathered a child, Anne Caroline, born in Orleans in 1792, ...
But in the meantime he had experienced a disastrous love affair. Not far from his own domain of Newstead (let for the moment, while Byron and his mother inhabited a neighbouring town) lay Annesley Hall, the home of Mary Chaworth, ...
It's correct to say that someone undergoes an experience. It's normally used for something unpleasant, to which your sentence conforms.
We often say:
"He's undergoing surgery"
"The building is undergoing repairs."
"He failed the exams and has to undergo another whole year at school."