It absolutely does stop SSH or Web traffic, if the network path goes through a link with MTU < 1500 and the connection comes in with MSS > PMTU - 40. But only, as the post says, once you start sending a lot of data in one TCP segment.
I've had more than a few cases where I couldn't SSH into a system at a hospital or clinic because the VPN/firewall/whatever that their connection went over rejected packets with too high of an MTU. Generally you'll get your SSH connection and it'll hang in the middle of the MOTD.
