edit: Disregard the below, some of the replies in the CJ Fabbro tweet seem to suggest CJ is wrong and Fabbro's 1st year is also burned regardless. That still doesn't answer the question regarding whether him and Woll would be expansion eligible without playing games.
Most guys burn the first year by playing a game though. Dante Fabbro(same draft, same age, same league/NCAA) for instance, just signed with Nashville and will only burn the first year of his ELC if he plays a NHL game this season, per Chris Johnston on twitter(above). Otherwise it's treated as a contract signed now for next season(which happens all the time, see Chad Krys, also same draft, age and league/NCAA signed a couple days ago) and not a slide.
I've never seen a guy signed in March, and guaranteed to burn a year off the deal without playing a game that season.