Welcome to the joys of old home ownership. We redid our master bedroom shortly after moving in 2 years ago. It's a big room (23'x14') and had 2 ceiling fixtures, one with a fan. I had to tear down the plaster & lath ceiling (huge mess), remove the old gas light lines, and have an electrician friend run new Romex and put in new boxes as it was all original knob and tube. All the outlets and 1st floor lights had been rewired already but the bedroom lights were left alone.
A lot of work for 2 new small fixtures? You bet. Was it worth it? Absolutely. No longer have to worry about the condition of the ceiling, the weird and possibly dangerous wiring, etc, and I know I can easily replace the new fixtures down the line.
The other bedrooms had dropped ceilings and were much easier to rewire, although its temporary until I work up the steam to do those ceilings too.
Could you attach the new fixture to what's there? Where there's a will, there's a way. Is it correct, legal, and safe? Nope.