Yes
A friend did track days by taking off the muffler leaving the crossover which is designed to scavenge the spent exhaust. He said each header isn’t big (wide) enough alone, but the crossover, being a split that widens the available exhaust space, acts like the exit side of the venturi. Guzzi has two venturi, one in front of the carb and the other formed by the exhaust and crossover
Taking off the crossover takes away the venturi effect.
I’ll be back with the right info from wikipedia…
https://en.wikipedia.org/wiki/Venturi_effectIn fluid dynamics it’s a Venturi. Same as air. My old brain forgets the term for that little piece in front of the carb that first constricts the airflow (same as fluid) and then expands to create faster flow
(my understanding is the exhaust pipes on guzzi are a little too small)
and then there is an expansion (the crossover that almost doubles the area for exhaust to both pipes) that make a scavenging effect for faster airflow, pulling the spent gases away faster then the piston can push into the exhaust header
So he suggests…i never went to track days. Ymmv

This also explains Guzzi moving the crossover closer to the exhaust valve to above the rotor/stator on the higher powered LeMan type bikes. With the header being stuffed by higher rpm usage, creating a need to split in the exhaust gas sooner, and also a second crossover below the transmission
Looking at the unmuffled exhaust of the La Franconi, here in the race bike foto, you can see the slowly expanding exhaust pipe as it goes away from the second crossover below the transmission This too has a scavenging venturi effect. Notice if you straighten this race exhaust you’ll have approximately the same length as your stock T3 headers, but without mufflers
The stock guzzi bits are pretty well thought out. Yes you can just remove the crossover but that removes the venturi effect.
Start your bike with just the headers and it makes a funny pop pop pop sound, not the explosive roar you might expect