This doesn't sound like a great idea. A friend of mine with an Indian passport and a valid UK work visa was visiting Northern Ireland and decided to try to sneak a quick bus trip into Republic of Ireland. Their bus was randomly stopped and everyone's passports were checked (these are pretty infrequent, I believe), the police quickly noticed they didn't have a valid visa for Ireland, took their details and then took them back to the North. Later that year he had a bit of trouble visiting mainland EU, the immigration officials cited his previous attempt to illegally enter Ireland - evidently it had been logged in some EU immigration database and can follow you around for a while.
And this is just Ireland, I imagine the repercussions of getting denied from the US are a little more severe.