Well, Section 31 at various times has been shown to have it's fingers in a few pies (and certainly in one incarnation was able to genetically engineer the virus that would kill an entire species if allowed to) so I wouldn't find it a stretch to imagine that they also are or become involved in specialised weapons as well.
However, one possibility could be that in the wake of the destruction of Vulcan (and as part of Marcus's plan to militarize and more aggressively defend the Federation from it's percieved threats that Section 31 was in part refocused to spend more of it's time - at that stage - in weaponising technology (such as the transwarp equation) and developing newer ones as well. Before the London cover site was bombed one of the torpedo's which later carries Khan's crew is visible suggesting it was perhaps developed there). There's probably not a lot of additional corruption that Section 31 would require given what it already seems to do and it operates under the authority of no-one but itself (notwithstanding the Admirals who know of it's existence).
So, the events of 'Star Trek' could have (and in fact would have undoubtedly) had an impact on Section 31's activities and operations.
'If the Apocalypse starts, beep me!' - Buffy Summers
'The sky's the limit.....' Jean-Luc Picard, 'All Good Things'
courtesy of Saquist