For the purpose of this post, full spectrum means a non-trivial number of frequencies within a non-trivial band. So human eyes aren't full spectrum within the visual range (each cone is wide band, they overlap and there are only three) but ten or twenty relatively narrow non-overlapping channels covering the full width would. I'm defining it up-front so that it's clear what I'm discussing.
I know that you can link radio telescopes over thousands of miles with a collecting area of a square kilometre. It's called SKA and it's currently being built.
Likewise, I know that you can build optical interferometers, but currently, none are capable of resolving a visual image.
Max Tegmark built a huge interferometer (either microwave or infrared, I'm unsure), the Omniscope, for looking at the cosmic background radiation.
But here you run into the first problem. The average distance to the asteroid belt from the sun is 3.2 AU, so we can treat our disk of radio telescopes as having a diameter of 6.4 AU and a circumference of 32.2 AU. Even if you processed the data on Earth, half that disk isn't visible, so you've got to transmit the data over unreliable, non-deterministic, low-bandwidth, high-latency links for 34.2 AU (distance to a common transmitter since there's only one deep space network plus distance to Earth). The non-determinism is the potential killer as you have no means of determining how to overlay the data.
The second problem is that even optical interferometry is limited. For full-spectrum, you've got to get it through UV and into X-Ray, and telescopes have to look over much narrower bands. I don't know if such telescopes are possible.
Given that a greater range of telescopes complicates data delivery (you've got more complicated paths to get the data from A to B because telescopes want to transmit their own data, bandwidth is constrained because you're using radio telescopes and interferometry still has to patch the data together), it's reasonable to theorize that you have a minimum number of relay stations elsewhere in the belt for the number of telescopes.
But you've now added the number of places that can collide with other objects, that can fail due to hard radiation in space, and that move unpredictably (N-body problem) relative to the telescopes they're relaying.
So we can say that there should be an upper limit, a bound beyond which either the telescopes can't be linked as an interferometer due to communications problems, where there's just no added value (an interferometer of half the size and twice the time base will see more), or where the probability of failure from any cause exceeds the value of the data obtained in the mean time between failures. The exact cause of the limit is irrelevant, although if there is published science on this, it would be good to see.
We can also say that there is an upper frequency beyond which interferometry is impossible with any known science. The reason doesn't matter, just the bound, although, again, the science would be good to see if published.
Because the asteroids move relative to each other, the change in the relative position of each obviously impacts the timebase (unless you create yet another mechanism for tracking position, with the unreliability that creates). The tools used in synthetic aperture receivers might be useful since you can in principle treat the motion as simply receiving on different spots on your fixed virtual dish.
If there is a function tying maximum size to maximum frequency, that would be wonderful, as then you can plot the full range of possibilities.
Otherwise, how large of a telescope over how large of a range of frequencies over how many bands could you have? Would you need to create an original ringworld (disconnected platforms in a ring) to build this, or can you utilize the asteroid belt with minimal impact?
(To clarify, this last bit is the question of interest.)