No. The payment is a gift to the U.S. government and is not recoverable. It creates no ownership interest, earns no return, and is not held on deposit. The processing fee is separately nonrefundable, including where an application does not succeed after vetting.
Nothing about this payment behaves like capital
The comparison people reach for is the immigrant investor route, and it is the wrong comparison in every respect that matters financially. Investor capital is placed at risk in a commercial enterprise, may generate a return, is expected to remain invested for a period, and can in principle be recovered when the enterprise is eventually sold or wound up. A gift to the U.S.
government has none of those properties. It does not appear on a balance sheet as an asset, it cannot be pledged, and it does not come back if the family changes its mind or if circumstances change. Advisers in tax and estate planning should therefore see the arrangement described accurately, because a payment characterized as an investment in one professional's file and as a gift in another's will cause difficulty later.
The nonrefundable processing fee should be budgeted as a cost of applying rather than as part of the price.