River Runner- Pressurizing the tank in that manner would not get anything off the bottom or any of the layer below the pickup. Sure , you will see all-gas flow, but underway water or gomph from the bottom could still mix in and be sucked into the system. Depending on the tank volume below the pickup that could contain quite a lot of water, etc..
And if there is a filter sock on the pickup. any debris remains in the tank or on the sock.
Much more effective would be to remove the sender and "polish" by recirculating fuel picked up right at the bottom and returned to the bottom to stir things up, with large polishing filter/separator in the circuit. Using a pump certified for use with gasoline of course and protected connections and switch well away from fumes. This assumes the fuel is not phase-separated e10 gasohol which should be removed.
I consider dumping filter/separator contents and reusing element only a reasonable emergency get-home measure if for some reason new spares are not available onboard as they should be on any boat. But sometimes the replacements clog and need to be dumped as you suggest, with some good risk of allowing particles to pass to the outlet side..
Hopefully, you you have the type of filter with a drainable bowl with potential to keep you going after a quick drain even though the metal bowl drains ( unless your engines are O/B's) are a PIA since they don't have petcocks. Unfrotunately, just that draining doesn't allow helpful refill.
As for keeping spare fresh filter-filling gas onboard, how about a sturdy quart can of already-stabilized straight gas Tru-Fuel or similar available at every hardware store? It's pricey, but then how often is it needed if you maintain fuel system as best you can?
I've had my present boat since 1995 and somehow have never once had to replace a clogged fuel filter/separator running about 200 hrs/year worth of fuel through 2 tanks and 4 filter separators . Knock on fiberglass.... But I do keep a couple sets of each type onboard and correct filter wrenches to potentially deal with replacement.