Monitor swap usage while mining. If you're not swapping there's no problem.
Still won't be a problem If you are using a hdmi capable monitor, even if you keep swapping the monitor your CPU will do the job to render the display without issues, 2gb is pretty low but not entirely bad
If you want to contradict someone, make sure you're right.
This isn't about display rendering, it's about mining performance.
Any swapping will affect mining.