LOOKING AT A HOME BUILT IN THE 1950'S THAT USES CLAY TILE UNDER FLOOR, WITH A LAYOUT SIMILAR TO HOT WATER RADIANT, WHERE THE TILE IS AT THE PERIMETER THERE ARE FLOOR REGISTERS. THE CUSTOMER WANTS TO ADD AC. MY CONCERN BESIDES AIR VOLUME IS POSSIBLE CONDENSATION FORMING ON THE CONCRETE FLOOR FROM THE COOL AIR TRAVELING THROUGH THIS CLAY TILE.
Probably best to place it in the supply duct to sense dew point potential and interrupt compressor call if it gets close.
VCP radiant eh. I''ve read about them, but never actually seen it.
It's not so much a case of "You got what you paid for", as it is a matter of "You DIDN'T get what you DIDN'T pay for, and you're NOT going to get what you thought you were in the way of comfort". Borrowed from Heatboy.
You may want to look at adding a separate system such as mini-splits. A lot of times, there's a great amount of leakage with those old under slab duct systems due to the earth settling under the structure.
I lived in house with one about 30 years ago and when I pulled the furnace I found the in-ground plenumn had a 2-3" gap all the way around it allowing air to blow under the slab. There was a temperature drop of 20* from the plenumn to the last register. The gas co. loved me.
You can choose to do what you want, but you cannot choose the consequences.