I wouldn't want my fee to depend on something I couldn't control. The other issue, of course, is where the fee comes from. If it comes from the grant, you either have to convince the funder to accept the grantwriter's fee as part of the project budget or cobble up the budget to hide the fee. I wouldn't want to do either. And if you're talking about a government grant I certainly wouldn't want to give them an fudged budget.
Audits do happen.
It's possible, I suppose, that an agency could pay a percentage or contingency fee out of another source of funds. This would solve the problem of explaining the expense to the funder, but it wouldn't solve the first problem I mentioned. I'd suggest either quoting a flat fee or an hourly rate, whichever you and the client are comfortable with. If you're looking for funding, don't overlook corporate foundations. The Federal Register is published every day of the year except weekends and holidays.