Not unless you consider every request needing to use disk swap "running" which I can assure you is orders of magnitude slower and terrible.
In my experience on Rackspace cloud 512MB instances are the minimum you should use for tiny production apps. Also, they're discontinuing 256MB on OpenStack - these were suitable for single-user dev instances, but I got more swap and or locking if ever attempting to run publicly with traffic. 512MB instances solved that issue.
Edit: Also I should mention I'm assuming you mean wanting to run a fairly standard stack, not a stack targeted toward tiny memory footprint.