Extended Content Verification (ECV) Content Check HTTP Health Monitor Receive String (2)

but since the Health Monitor isn't working, would I expect any traffic to be processed?

yes, monitor should keep sending traffic at every interval.

I currently don't see any traffic processing. Also, how long should I run the dump?

is tcpdump filter correct? you may try to alter filter (e.g. remove non-floating self ip, remove port, etc) to see if you can get traffic.