LOL! No you can't. Unless a lucky arrow hits Harold in the eye, which I haven't had happening in my last attempt.
I've had a successful battle at York instead. Your starting forces are actually enough to defeat Harold's stack about half the time you try.
If you want to have the battle in Sussex, then you have to wait quite some time before he bothers to counter your invasion. If he does just hire a stack of mercs and converge on the battle with your entire force. Shouldn't be any problem to win that.
That's why I'd recommend taking all holdings in each county, it prevents them respawning behind you. Apart from that, just kill them before they have chance to group together if you can, it's not too hard.
You have to occupy all the counties in a province to prevent the armies from spawning, and that takes on average about 3 sieges/province.