What purpose did Quaid serve Cohagen as an Average Joe on the assembly line?

If I recall correctly, in the 1990 movie the resistance leader could tell if someone's mind had been tampered with. So Cohagen needed to create someone who was a part of the resistance but also had a legit reason for mind tampering. This is accomplished by capturing BW-Quaid and re-brainwashing him. From there, Quaid needed to find his way back to the resistance, but there needed to be an active perception that Cohagen didn't want him getting back to the resistance, thus the "wife" who's trying to stop him. And, once everything came out, the mole needed to be someone who would give the info about the resistance to Cohagen, thus it needed to start with someone loyal, like Quaid.

I presume this is also correct for the new movie.

I can't say anything for the 1990 version, but I don't think step 2 was included in the 2012 version. I could be wrong, but my understanding was that Quaid worked for the rebels knowing he was a double agent. The video recording that was activated by playing the piano had Quaid stating that he was Cohagen's agent with the mission of getting close to and killing the rebel leader. He said that this mission changed when he met Melina, and she showed him the "truth" about the rebels. So, we are lead to believe that Cohagen realized Quaid had turned, so he gave Quaid the false information about the kill code as an unknown source of disinformation. Then, to make the disinformation seem real, Cohagen captured, brainwashed, and hid Quaid from the rebels. By doing this and having the "wife" complicate things, he made it seem that the info Quaid found out was very important. Once the rebels got the "average Joe" Quaid to the rebel leader, they tried to access the information about the kill code in his brain. But, this just allowed Cohagen to trace the location of the rebels, since the code doesn't exist. In the 2012 version, it seems that Cohagen played Quaid from day one.

So, for the 2012 version, the purpose Quaid served as a factory worker was to be a "trojan horse" and unknowing double agent after he was brainwashed. This allowed Cohagen to pinpoint the rebel leader's location and kill him.

Have you considered the possibility that the film was not real and actually was the dream that Quaid bought?

That would explain why everything happened the way it was explained in the sales pitch and why the girl on the monitor when Quaid described his perfect girl looked exactly like the girl he met on Mars later.

Otherwise there was a very low chance of the plan actually working as so many co-incidences had to line up and that does not include the fact that Cohagen's henchmen did not know the plan and kept trying to kill Quaid.

I'm not sure about the 1990 version, but I just watched the 2012 version. This is what happened:

1. Quaid was working for Cohagen to infiltrate and kill the rebel leader, Mythias(?).
2. Quaid met Melina, then fell in love and was convinced that Cohagen must be stopped.
3. Quaid was captured by Cohagen's men (showed in the beginning), THEN GOT BRAINSHED into thinking that the bitch cop was his wife and that he was working at the factory.
4. BW-Quaid regains memory when he goes to the Rekall shop because he wanted a double-agent memory, but since he actually WAS one, cops showed up, he reacted by killing the cops, then started to run away.
5. The rest is him just finding out about his true identity and stopping the Cohagen's invasion.

Now, to answer your question. My guess is that Cohagen knew the rebel would look for Quaid and try to convince him to give them the nonexistent "kill code" for the "synthetics." This also works because if the plan had gone smoothly, then no police would have gotten hurt or killed.

My take on the 1990 version is this:

1. Quaid was working for Cohagen.
2. Quaid agreed to be brainwashed to think he switched to the rebel side.
3. While with the rebels, Quaid fell in love and his sympathy for the rebels became more innate.
4. Quaid, worried that he might be captured, made the video for himself telling him how to remove the tracker, etc. Whether he knew then that he was a double agent is hard to say. Maybe his inner training just took over and he did not know.
5. As Quaid feared, Cohagen decided to pull him out, but loved him like a son, so he had him brainwashed again instead of killing him. He placed people close by to keep an eye on him. In short, he didn't serve any purpose as "average joe" except Cohagen didn't have to kill him.
6. The Rekall thing was just really bad luck for everyone, except that clearly his fascination with Mars had some basis in his inner mind.
7. So the effort to get back and rejoin the rebels was genuine, and so was Cohagen's attempts to stop him, but once again he did not want him killed. Maybe because he loved him, and maybe because he was already thinking he might be able to use him, but what he SAYS is he wants him reimplanted and put back into the same cover situation. I think Cohagen just cared about him.
8. But once Quaid made it to Mars, Cohagen also put someone (taxi driver) on Quaid to try and follow him into the rebel center, and it worked. This was never the master plan, but a way to salvage the original goal.
9. When Quaid learns of his original identity and goal, he rejects it, even though there is yet another video he made for himself.