no, and yes.
NO do not dryclean foam (if you could FIND a drycleaner who would do it)
The likelihod is that the foam is not compatible with drycleaning chemicals.
You would be better off trying to replace the foam.
I got an Old Fat Boat
She's Slow But Handsome
Hard In The Chine, but Soft In The Transom
I Love Her Well, And She Must Love Me
But I think It's Only For My Money
. ..... Gordon Bok