If you wanted to build a Dyson sphere you would capture all the light from your star and might not exhibit ANY radiation.
We wouldn't see such a species and if there's such a small blink of time between the industrial age to the singularity the probability that there is an overlapping species is very very low.
We would only have about 20-40 years to actually have the technology to find them before we hit the singularity.
We have NO idea what happens after that point but my plan is to just chill with my wife in a virtual Yosemite park once we hit the singularity.