A couple remarks...
First of all, water only flows uphill against gravity on Uranus (cue the laughter and applause), but in your case, you have a larger drop behind it pushing the water up, so it'll work.
I would recommend though that you use quite large pipe, and arrange it like a standpipe in the wall with the hose from your overflow stuck into it... sorta like the drain standpipes that washers hook up to. That will allow air to circulate freely in the pipe and will prevent gurgling from your overflow. Since your filter end the pipe is "sealed" by water, you need air to enter from at least one side. If you like, to reduce humidity and noise, you can stuff filter floss into the space between your overflow hose and the standpipe outlet.
Also, you should try to pitch the pipe downward at a slope of maybe 1-2" per 10 feet of pipe run, so the filter end is 2.5" - 5" lower than the tank end. This will encourage the water to flow towards the filter and will minimize stagnation in the pipes (though at 1400gph that shouldn't be a problem). Finally, at the filter end, I'd put a drain plug, allowing you to completely flush out the line in the event that gravel, detritus, etc builds up and fouls your water or impedes your flow.
Another thing you may want to consider is to put a "T" at the low point in the pipe, just before your filter, and run it to a pipe that exits the side of the house with a ball valve. This will allow you to open the valve and use the pipe as a drain into the yard, so you can siphon water directly into your pipe when doing water changes... a nice little "feature."
You are gonna need a heck of a pump to get 1400gph after a 25 foot run and what will probably be several elbows.... something to consider with what PGE charges for electricty :thinking: