Jed, it'll likely not come too much wether you collect shots for them or not. Comply or don't comply based on your convictions. But if it's a moral question, it seems like you'd try to steward the wishes of the company as best you can, "ride for the brand," Louis L 'Amour would say. That said, collecting footage is only the 1st part of the effort to build a company presence online. It's difficult to sufficiently capture a concise, coherent sequence of work through the tiny keyhole of a camera lens. Job site dynamics need focused effort to bottle up, even the most simple jobs.
Then if that footage makes it all the way through the many pitfalls of human and technical error, clear to a capable editing program run by a capable editor who possesses the same job site intelligence that was able to gather it. . . Then, and only then, there is hope of watchable content after some patience splicing it all together.
If you decide to participate, there are ways to keep it reletively painless for yourself and for the editor.
Don't run the battery dead and plug-load the micro-SD card capturing everything. Just capture the highlights within your areas of the job from beginning, middle to end. Short clips. This way your battery will last through the whole project and your clips won't take up a vault of storage space. The number one killer of a tree video's journey to the web is the patience and knowledge of the editor. If he/she has too much material to sift through, then it'll often drag editor resolve and resources to a halt.
Initially, it's likely your company would be better served by ONE camera in the hands of one capable story teller who passes it around at the pertinent times to collect the highlights of sequence. His job is director/story teller. He stops people, starts people, makes people repeat things, sends the camera up, asks for it back, reminds them to start and stop recording etc. He imposes on the patience of everyone around with dogged commitment to the "production" that lives on long after the moment/job-site production is gone. Think of Beranek making all those production loggers stop everything and pose. It's no different than that unless it's even more imposing because its video. If they can master decent story flow with one camera, then perhaps they can step up to multiples.
To reiterate, it sounds like currently your part can be very simple; capture short clips of action AND INTERACTION along the sequence of the job and then give them back the camera. Human interaction adds watchability to the hum drum of over-action.
After all that, even if they produce a decent video or two, a successful channel will only be built through long term dedication and only those with the heart of a story teller will have that. Your part can be easy though.