Technically, no. Not that you can’t separate liquid from cells after adding anticoagulants. But serum is defined to be the liquid phase after allowing the clotting system to work. Serum will be depleted of clotting factors and other proteins or metabolites that are extremely unstable for one reason or another. You can add things like citrate as a preservative, I think, but not EDTA or heparin; if you inhibit the clotting system you will be separating out plasma, not serum.

If I remember correctly (and I may not, so it would be wise to confirm this) clinical samples are left to clot at room temperature for something like 20-30 minutes before spinning them down and removing the serum.

In theory it takes less than 10 minutes(as it is defined by physiology books, with formation of tromboplastine being the most time-demanding phase). But in general labs leave it for more than that just to make sure the reactions have all gone to completion.