You'd have to ask the issuer if any tax will be withheld.  But if so, then yes, you would get it refunded back to the estate.

You'd enter the income on Line 8, Other income line of the 1041, and the withholding will be entered on the 1041 Page 2, Sch G, Part II, Line 14 and you'd check the box that it's from a 1099.