The whole scenario seems unlikely. How would he not have children to support? And no alimony? I guess it could happen, but there would also be a scandal factor of someone with a failed marriage. Then you'd also have to wonder how old someone would be by that time in his life. Seminaries often have a maximum age at which they will accept a candidate.
There are divorced men who do not have children to support, and alimony is more or less an outdated concept. Many marriages fail fairly soon after they take place (at least in the secular world), and the man would not necessarily be that old.
The "scandal factor" would probably be the most logical reason not to ordain such men. I'd like to see Catholics be broad-minded enough to realize that Almighty God does not always call perfect men with perfect lives, but that might be a bridge too far.
And just to clarify, I am not asking for myself. Even if I did perceive myself as having a vocation --- and keep in mind that no man is "called to the priesthood" until his bishop summons him forth on the day of ordination,
that's the "vocation" part --- I am far too old for any seminary to take me, and I have responsibilities that won't vanish the day my son turns 18. Very few families anymore turn their children out on the street anymore at age 18 and say "we've raised you, now you're on your own".