Usually not.

There have been some employers who forced furloughed pilots to submit a resignation letter to the furlough airline... they would typically write the letter for you, make you sign it, and then mail it on your behalf.

There were also some airlines who just ignored those letters, and one or more have union contractual provisions such that you cannot resign while in a furlough, to protect against this sort of thing.

As far as seniority goes, it stays where it was relative to other furloughed and non-furloughed pilots. Your longevity usually stops, and then resumes once recalled but IIRC some airlines actually keep your longevity progression (so a 3 year pilot who is furloughed for two years would return as a five year pilot for pay, vacation, etc).

Now there is one way you can lose big-time seniority on furlough: Merger.

If Legacy A furloughs 30% and ULCC B furloughs 10% and then they merge, ALL furloughs will be stapled below ALL active pilots. So a 2015 legacy hire could come back behind a 2019 ULCC hire. It's important to make sure your airline doesn't merge while you're furloughed.