And actually, La'an's backstory FIXES a interesting issue with TOS S1 "Arena" in that - In the opening Teaser Kirk is conversing with (supposedly Commodore Travers live over a ground to surface radio link in the 1701 Transporter Room:
http://www.chakoteya.net/StarTrek/19.htm
KIRK: Scotty. Kirk here.
TRAVERS [OC]: Travers, Jim. We're waiting.
KIRK: Good, Commodore. We're on our way.
TRAVERS [OC]: Be sure to bring along your tactical people. I've got an interesting problem for them.
KIRK: We'll beam down immediately, Commodore. Kirk out.
SPOCK: Captain. I wonder why he's insistent that our tactical aides come down.
KIRK: This colony is isolated, exposed, out on the edge of now here. He probably wants additional advice.
SPOCK: Perhaps, Captain, but nevertheless
MCCOY: Spock, isn't it enough the commodore is famous for his hospitality? I, for one, could use a good non-reconstituted meal.
SPOCK: Doctor, you are a sensualist.
MCCOY: You bet your pointed ears I am. Ready whenever you are, Captain.
(Six men, including one red shirt, get on the transporter platform)
KIRK: Energise.
[Planet surface]
(There is no one waiting to meet them. Instead, just razed ground and the smoke of a few fires)
KIRK: Kirk to Enterprise. Red alert.
SULU [OC]: What is it, Captain?
KIRK: Cestus Three has been destroyed.
(They take cover)
So yeah, to be able to do that the Gorn seemed to have A LOT of specific info on Starfleet that I doubt they got from the base as from later dialogue in "Arena" the Gorn just wiped everything on the Base out completely. The Base even offered to surrender, but the Gorn just kept going and killed everyone and destroyed everything. So yeah, the Gorn had to get that info from somewhere - and it appears it was by capturing Star Fleet ships that ventured into their space.
And YES; Kirk decided not to kill the Gorn, and (presumably) later, a diplomatic dialogue was established - but during the incident, The Gorn Captain seemed to have no qualms about killing Kirk (and the Enterprise) - to wit:
KIRK [on viewscreen]: Who is this, the Metron?
GORN [OC]: This is your opponent, Earthling. I have heard every word you have said.
KIRK [on viewscreen]: All right. What do you want?
GORN [on viewscreen]: I'm weary of the chase. Wait for me. I shall be merciful and quick.
So yeah...No...IMO, the Gorn (even AFTER obtaining a lot of personal and personnel info - enough to make many a convincing message to lure the 1701 there; the Gorn intent was to test/destroy Federation/Star Fleet military tech capability. With all the info they obviously had - IF the Gorn wanted to open a diplomatic dialogue with the Federation/Star Fleet, they could have done so before the Cestus III massacre. Hell, they could have arranged via the staff on Cestus III.