Don't count on it.
No longer a flat tire "rule" but more senior agents at the airport may exercise discretion under the same principle.
If they don't and you are flying on a standard domestic penalty fare, your ticket (including return and onward segments) may be cancelled and retain whatever value it has under its fare rules (generally $0). That leaves you purchasing a new ticket at even higher prices (if there is space).
I would leave 'flat tire" for situations where there really is a flat tire and not to game ticket pricing. The latter can get quite pricey.