I think the answer is that yes it MAY be a problem
it depends on a lot of factors...sadly the most important IME is the type of child they wish to adopt. Its more of a problem if you wish to adopt a healthy baby, toddler or pre schooler. If your relatives are able to consider a child with special needs, or a large sibling group or school aged children, or if they are a black family, it will be less of a problem.
you might well ask, of course, why those adopting "easier" children need better health than those adopting more challenging children and this is indeed a good question
it will also depend, as other have said , on your relatives health. How often he has been ill and for how long, how long ago, his specific diagnosis & treatment, his prognosis etc etc. He will require a detailed medical report from his GP and also his psychiatrist. I would suspect that if it is an ongoing illness then it might well prevent them from adopting
Unfortunately issues such as a history of depression and obesity, which used NOT to be a problem, are now proving to be so with some panels.
If it were me i would wish to be raising this issue at a very early stage, in writing, with a senior officer in the agency. what I would not want is to get a year / eighteen months down the line then be turned down / put on hold before panel. If you search through the adoption threads you will see this has happened to several Mners.
I would not repeat NOT be satisfied with a verbal assurance from a junior Sw that "I'm sure it will be fine" or "we'll talk about that later".
HTH