The simple answer is yes. It will work as a dumb trigger.
I have one connected to the winder grip of my ETRS and it triggers just fine.
It won't have the speedlight wake feature as that is tied to the auto focus confirmation but on mine I just opened the bottom up and took out all the extra contacts apart from the X sync as all I need it to do is remotely trigger the flash heads. I can wake the lights up by pressing the test button, no biggie.
BTW I do use it on all my old manual 35mm cameras as well, it works on everything that has the capability to sync flash.
I turned off the sleep mode in Speedlight sometime ago. :-) Many shots were missed when I try to use with OM-1n.
OM-1n: Do I need to own a Leica?
Rolleicord Va: Humble.
Agfa Isolette III: Amazingly simple, yet it produces outstanding negatives.