Hello Crispin
I haven't tried it, but I assume that EyeFi will probably not work. The camera generates the AVI film from the individual images only when the recording is interrupted.
I am currently running my camera on a construction site. It currently takes a picture every five minutes from 6.30 a.m. to 6 p.m. every day. At about 15 frames per second, this makes a nice construction site souvenir. I take the pictures about every second weekend. In terms of battery life, however, much longer intervals would be possible without any problems.
But "live" monitoring is of course not an issue.
Kind regards and have fun with the construction site and the camera ;)