[jg42]

Sort of. The "rules" to establish a contact generally state that you have to exchange some data, but doesn't define "data". Mostly this devolves into a simple piece of data - your grid coordinate is one example. During contests (yes, there are amateur radio contests), a signal report (strength and clarity expressed as 2 digits) would be accepted.

With a low bandwidth mode like this, there is not much possibility of transmitting more than a few bits of data. So a grid square and callsign are about all that will fit.