Zack is *very* interesting to Shinra from a scientific standpoint (there is some... very ironic dialouge between Zack and Hojo in Chapter 3 of Crisis Core in the SOLDIER Training Room). Especially to Deepground. He's an anomiliy in a lot of ways when it comes to Jenova (for one) and he's got a very werid LImit Break that allows him to copy other's abilities due to that. Deepground would want him for just that reason alone. The only other person we know who somehow can... aquire... other people's abilities is Weiss, who has all the special abilities of the other Tsivets. He just... doesnt need Jenova to do that.
Deepground is very opportunistic when it comes to acquiring people. People are constantly dying down there due to be experimented to death (literally). And anyone who survives that is thrown into a very cut-throat environment where it's... essentially all about being stronger than everyone else who wants to kill you. And Deepground is in the buisness of making supersoldiers. Zack is... basicly the most powerful *known* person in the world at the end of CC. He's stronger than Genesis at least which... sticks him up near Sephrioth's level. And Deepground was interested in Genesis (who was too powerful for them to actually *keep* in Deepground).
It's... kinda a no-brainer that Deepground would be interested in Zack just for that reason. And also because Deepground has a problem when it comes to Weiss. Namely that Weiss is *too strong* and they're worried about losing control of him. Trying to find someone stronger than him to keep in check would be a good thing from their point of view (not that Zack would help them out or anything like that).
If I were to do it, I would have Zack get taken down by surprise. Kind of like how the mall cop equivalent Cloud managed to sucker punch Sephiroth himself in Nibelheim. Just get a Turk to use some sort of disabling weapon or technique from a distance, in a stealthy way, and knock out the weakened Zack. Reno vs Cloud was more of a straight duel, but this would be just like getting sniped.
You are not the first person to suggest this. I know of at least one fan-fic that has... exactly this happen with one of the Turks shooting a load of tranquilizers at Zack for this exact reason.
The Turks really don't want Zack dead. And that is more than just "we're both against Shinra right now". Both CC and BC establish Zack and the Turks going on a few too many (bad) missions together that they... aren't just work acquaintances anymore. The Turks are presented in BC as regretting some stuff they've done, but Zack and Cloud ending up with Hojo is the only thing they feel bad enough about to actually trying to *fix*. It's further complicated by the Turks (especially Tseng) knowing both Aerith and Zack and going... way out of their way to avoid bringing either of them in.
Incidently, letting Zack and Cloud go is the first time the Turks *really* go against Shinra's direct order (you might consider this the second time if the firs time is how they don't turn Aerith in for years). This happens a vew days before they run into Veld again and let him go, which is when Scarlet catches them and finally declares them all traitors to Shinra. They then spend the next ten months being hunted by Shinra and... amazingly not getting caught by them. The entire time, they're looking out for both Veld and Zack and Cloud in the hope that they can find them before Shinra does. And they're holding Rufus hostage the entire time... on paper. Really, he's integral to them finding Veld at all.
The way the timing works out... Zack dies before the Turks get back into Shinra's good graces (and they arguably never actually do this... it's more Heideggar not being able to kill them because Rufus really isn't a good person to make a political enemy out of). Rufus has spent... the last four years with the Turks under house arrest. And by the end of it, he was passing info from Shinra to them *on purpose* and with full knowledge of what they are actually doing with it. There's... no reason he wouldn't know what the Turks were planning *not* to do with Zack. Like... Rufus was pretty much in their base of operations the entire time they were looking for Zack and Veld (around ten months)... and not because the Turks were forcing him to be there either.
I see Rufus not looking the other way for the Turks helping Zack going... very much against how he is presented at the end of Before Crisis (and in Case of Shinra). Whle Rufus is a pragmatist, he also isn't so stupid as to not get how loyalty to other people works. And I have a very hard time seeing him not realize the Turks are loyal to Zack in a certain way. Esspecially as Rufus being understanding about Zack not getting killed has the possibility of him not making an enemy out of Zack in the future either... and it would only serve to give the Turks good reasons to let him keep being their boss.