I volunteered in March '18 and was part of the class of '18 with a severance package. I talked directly to my VP about this and he was a little non-committal at first but was supportive. In the end they were happy to have volunteers so others could stay.
I heard stories of other VPs that didn't want to take volunteers...leading to some employees feeling really trapped.
I don't think I would recommend this route unless you ultimately are willing to leave without a package. There is about a 50/50 chance it will work out. In my case it did, but I had had enough of this place and would have left either way.
You have to approach this from a position of strength and be willing to deal with the consequences.
Without knowing your financial position and job prospects it's hard to offer an opinion, but I think you will figure it out.
I think the Q is in for some very rough waters and for many getting out now would be best.
Think that this is some good advice given by the OP @VMdMx8A-cyl