I have implemented a VGA controller in FPGA, for 800x600 resolution @60Hz. Can I use it to drive a PC monitor ? In the PC's monitor resolution settings, it's seen that it supports multiple resolution at different frame rates, including 800x600. The maximum is 1024x768. Its an LCD monitor. Will the PC's monitor automatically "figure out" the intended resolution and frame rate from the Hsync and Vsync signal of my VGA controller, and display it in full screen?
Your monitor should auto-detect the resolution. You can eventually double-check this by hooking it to a PC with a VGA output, and force the screen resolution to 800x600. You'll see that the monitor will scale the image.
This scaling is done by the monitor, not by the video card. There is a "scaler chip" inside TFT monitors that takes care of that. More details can be found on the internet.