Brake job?? You mean brake adjustment? If you are actually doing a brake job, with hub disassembled, then I'd hand pack at this time, and not add grease for several years.
Otherwise, your plan should work to do a complete check every 5 yrs, depending on miles/use. The obvious though, a brake problem, a hot hub after towing, needs to be checked out.
I have used the EZ lube on 3 different trailers. I did find one seal that was leaking, causing some contamination, while doing a complete inspection. So yes, it happens, but I am not afraid to use the system as designed.
Jerry