No, at my company the FE's did not touch the throttles at all. Some airlines had a different policy.
Generally FE's on the ground were responsible for the "walk around" inspection, ensuring all fluids quantities were correct (engine oil, etc.) and interior aircraft inspection (O2 bottles, fire extinguishers).
Inflight they monitored and adjusted the electrical, hydraulic, fuel, pressurization and air condidtioning and secondary engine systems/indications. They maintained the FAA required contact with Company dispatchers, monitored weather enroute and at destination and computed all performance data (max cruise altitudes, approach speeds). Secondarily, they dealt with passenger problems in the back and did minor "fix it" stuff for the Flight Attendants... like finding the circuit breaker for the galley coffee maker and resetting it.
In event of an inflight emergency, the FE read the checklist and made sure everything was accomplished in the proper order and double checked switch movment as the steps were followed. Many of the E-checklists consisted of mostly FE duties... like manual lowering of the gear on a 727.
Then there's the fact that they also provided "another set of eyes" in the cockpit. Always handy in high density traffic areas and always welcome during the really nasty instrument approaches.
Now without them on board, some things have been automated and some things have become MUCH more difficult. Some things just don't get done so they reclassified them as "unnecessary". IMO, in the really serious inflight emergencies in bad weather the FE is missed. But that's a rare situation and the bean counters accept the risk... because nothing happens to them.

But hey, getting rid of the FE's saved about $5 a ticket....... maybe not quite that much.
