How large was the Federation supposed to be? 

In Space Viking, Otto Harkamen says the Old Federation occupied a sphere of 200 billion cubic light years. That would be a sphere with a diameter of 7.2 billion light years. 

Ships at the time of Space Viking had an average speed of a light year an hour, so supposing that a faster ship could go hundred times that or 2400 light years/day, that means it would take more than 4100 years to cross the entire Federation assuming it was even-sized sphere.

Now the Milky Way is only 100,000 light years across so was Piper postulating an extra-galactic Federation that spanned galaxies?

"You know, of course, how big the Old Federation is. You know the figures, that is, but do they mean anything to you? I know they don't to a good many spacemen, even. We talk glibly about ten to the hundredth power, but emotionally we still count, 'One, Two, Three, Many.'
Otto Harkamen