Will a 70-76 A-body knob style radio fit properly in a 70 B-body with a rally dash?

It will work, I had an am/fm out of an A Body in my 70 Charger for a while, the front lens part will not fit your radio bezel right as it is flush with the radio in an A Body.

It can be made to fit , but it certainly is not a straight bolt in.
The main mounting diffrence you will encounter is that the 70 b had bolts in the front of the housing mounting the radio into the metal dash frame, the A body has threaded knob shafts .The mounting stud location will also differ, with the 70 B being on the back , and the A on the side , so you will need to fab a bracket. Of course as far as cosmetics they are very diffrent . Lense design/shape, push buttons, dial face etc all differ , but you will save a half a grand .
I have some pretty good up close shots of the front of the 70 B AM FM as well as the A body AM FM that you can use as a refrence to see the mounting diffrences you can expect to encounter.
Look at the radio gallery page to see some good pics .
http://wardsclassiccarradiorepair.com/

Greg