If a monitor's max resolution is for example 1600x900 and if the video card supports resolutions upto 2560 x 1440, then will those resolutions beyond 1600x900 be displayed on the screen resolution options at all?
It depends on the card and driver involved. Some cards/drivers will allow you to select a larger resolution. But only the portion supported by the monitor is shown at one time and the "desktop" can be scrolled to the sides and up/down to reveal the portions not shown. Either way, however, maximum that can be seen at one time will only the largest size supported by all three items involved (card, driver, monitor).