No I would not marry someone with a cold sore, regardless of how much I loved them.
The second I saw it I would dump them, force them to move out, start taking showers 3-4 times a day, picket both her house and her parents, start a website for survivors of cold sore abuse and lobby the government to remove the citizenship of any people confirmed to have this plague.
Should the government be unresponsive to my demands for purity I would create my own political party "ClearLips of America" and run for office. If defeated, I would solicit funding for a revolution and try to overthrow democracy with force.
Either that or I would get over my shallow hangups and marry her if I loved her.
One of the two, it's a toss up.