They would have had to construct and deploy a relatively new technology very rapidly, and while they would have had some kind of idea of how it worked, I doubt they actually got a full set of technical information.
I also really can't see the GTVA, given what the Shivans have done to the member races, being willing to talk to them. Or for that matter, even seeing the point to trying to talk to them in the time period they would have (possibly) had the capablity: what could the GTVA really have offered that the Shivans and their 80+ Sathanas juggernauts weren't capable of taking with ease?
There is an additional and very important reason not to talk to the Shivans: it would give away the fact that the GTVA can understand them, which would make future monitoring of and combat against them much harder. Given what the Shivans did aboard the Iceni, it's possible that they themselves realized this made them vunerable and attempted to destroy all evidence of the ETAK device at a more fundemental level prior to destruction of the Iceni itself. (Perhaps due to the Iceni's heavily-armored nature and apparent heavy redundancy and compartmentalization, they did not feel sure that destroying the ship would definitively remove all evidence.) So far as we know, the Shivans remain blissfully ignorant of the GTVA's ability to eavesdrop on them. Total mastery of an enemy's communications can bring vast benefits, and this is an advantage that would not be discarded lightly by Terran strageists (who would remember such battles as Tannenburg and Midway). Only if the situation approached total panic would the military likely be inclined to look favorably on attempting to talk with the Shivans, and it does not seem that things ever got that bad at the command level.
I've speculated before that Bosch discovered the Shivans couldn't be swayed from wiping out the GTVA, and in an effort to save humanity (as he's always been in this, at least in his head, for the good of his species) lied to them about GTVA capablities and force size, provoking the Shivans to destroy the Capella star as a means of sealing themselves off from a supposed Terran-Vasudan superpower. (Which would make the apparent sacrifice of a number of juggernauts a more rational decision, as the concept of acceptable losses tends to get bigger compared to the alternative of possible annihilation; the same philosophy drove the GTVA plan to collapse the Capella nodes. It would be ironic if both sides were thinking much the same thing.)