It depends a lot on whether or not the person is willing to do their best to manage the mental illness.

Take my biological father for example. He clearly has mental illness problems, has my whole life, but he always refused to get proper help. He turned to drinking instead, became an alcoholic and even developed some alcohol dementia. Even without his mental health problems, he is a nasty, entitled person, takes no responsibility and his life has been one massive train wreck that he is always trying to suck other people into (so that he can use them).

Then you have schizophrenic people who are the polar opposite. They are empathetic and compassionate, and want to do everything they can to not hurt others. They take responsibility and try their best to manage symptoms. They're willing to try medications until they find the right one(s), and stick with it. They're open to proper communication that allows them to share a functional relationship with others.

There are also different type of schizophrenia, which can make a huge difference. Schizoaffective of course means mood swings, which implies that she doesn't have negative symptoms or "flat effect". Some people with schizophrenia suffer from a flat effect, become extremely withdrawn and are unable to truly interact with others in a meaningful way. This manifestation is especially tragic and would make it extremely difficult to have a relationship. However some schizophrenics experience more so positive symptoms like paranoia, hallucinations, delusions, etc, and it's a matter of getting those symptoms under control while leaving the core emotions and personality in tact.