Unfortunately, most stores and SFS are like that. When the lead (whether they have a Fulfillment lead or another TL) looking over SFS is off/gone it's usually ignored by the other leads. The only people that seem to watch it would be the STL or ETL LOG, but not all stores prioritize ship because it's still a relatively small portion of the business.
I would take charge as much as you want. Nobody is going to test you really, so if you're trying or at least considering moving up, the best way to show you are ready is to do the job you want, even though you don't actually have it, yet.