No. If you centrifuge whole blood first and then add the resulting cell pack onto Ficoll, it would disrupt the necessary density layers and prevent the proper separation of PBMCs.
You need to add the whole blood onto the density gradient medium (like Ficoll) and then centrifuge it to separate the PBMCs. This standard method of density gradient centrifugation, relies on Ficoll's specific density to create layers of blood components after centrifugation, with PBMCs collecting at the interface of the Ficoll and plasma layer.
My answer would be yes...but you need to dilute the cell pack and marry back with the blood/PBS mixture before overlaying on the density gradient medium. Specifically, I have taken ~5mL of whole blood and spun @ ~350 x g to loosely pellet the cells (RBC + WBC) and then I collected ~2mL of plasma off the top and transferred into another tube (to be spun "faster" to collect plasma). I then added 5mL of PBS to the cell pack and gently suspend with a serological pipet before adding this "suspension" back into the whole blood (pooled into a 50mL tube). I then diluted the blood ~1:1 with PBS before overlaying on the density gradient and proceeding according to SOPs.
I’ve used this approach with several protocols, and it works well. It’s especially useful when you need to run multiple tests on the same patient or participant, since you can avoid collecting multiple tubes